Saffron is the Worlds most expensive spice, some varieties sell for as high as $1500 per lb , even the common household version of Spanish Saffron from McCormick is currently selling for 17.92 per Oz. that's a hefty price for an herb. The only other herbs you can grow, that attain anywhere near that price are illegal.
True Saffron spice comes from the stigma of the Saffron corm flower [Saffron Crocus], yes that is c-o-r-m, not corn. The corm is the bulb from which the Saffron is grown - it is a rounded tuber that produces up to 3 flowers. The Saffrom spice itself comes from the stigma of the plant which is part of the flower, and a very small part at that. Each flower will yield up to 3 strands of saffron.
It takes roughly a pound of fresh flowers to yield an ounce of stigmas. Once the stigmas are dried to produce the spice, it loses about 75 - 80% of its mass and substantial weight leaving you with very little spice, which is one very good reason the price is so exorbitant. In addition to its culinary uses Saffron also has pharmaceutical, cosmetic, and industrial applications.
Saffron is a tough crop to grow but far from impossible. In fact it is probably easier to grow hydroponically than it would be conventionally. The bulbs or corms are easily obtained. - See - Saffron Corms.Bulb quality, Growing conditions, nutrients and a wee bit of luck will determine the quality and volume of the yield.
In a normal natural outdoor setting they are planted in the ground, either in late summer or early Autumn.
In an indoor Hydroponic scenario they can be planted continuously as you are determining and manipulating their environment.
The corms can be planted, flowered, and harvested in roughly 45 day cycles. At the culmination of each cycle you will have to start with new corms or wait for the existing ones to go through their vegetative and dormancy phases before re-flowering and producing again.
The non productive vegetative and dormancy phase takes roughly 9 months, so starting with new corms each cycle is actually the most cost effective route.
Another option is to keep several sets of corms and their daughter corms, while one set is dormant the others will be producing.
Dormant Corms should be stored in a dry location and planted out at the appropriate time.
They are cold hardy - so can actually be planted out over the winter and will sprout again in the fall. They do need to go through their vegetative stage to shore up enough energy for production of the following seasons crop.Each healthy parent corm should produce 5 - 10 daughter corms that can be used to produce another crop in the following season.
Grow Media - Starter Trays
If you plan on getting heavily involved with growing Saffron or similar plants hydroponically you may want to consider pin trays that hold the bulbs in place. 
They were designed for forcing Tulip production in the Netherlands and work well for starting similar plants such as Saffron Crocus. They are basically temporary growing chambers where the plants roots will be growing and the bulb anchored. They provide support while the roots are developing and are only temporary.
Once the roots develop it should be moved to a more flexible media to prevent damage to the bulb.
You can also start the bulbs in Oasis Cubes which are more readily available than the pin trays described above before moving them to a more suitable media. A sterile and loose growing Media such as Perlite, vermiculite - perlite blend, coco coir, Higromite or etcetra is necessary to anchor the plants about 2 inches deep. The Media should be loose enough to allow for bulb and root expansion but sturdy enough to support the full grown flowering plant.
Plants should be spaced roughly 4 1/2 inches apart give or take a few nano meters. Flowers actually form within the womb of the corm during their dormancy and spring out in the fall- yes fall, as in Autumn, they spring out - but not in the spring.
Flowering is initiated once the temperatures begin to decline and enough moisture is provided. In a hydroponic scenario, moisture shouldn't be an issue.
Temperature must be manipulated by the grower. A 60 - 65 F daytime range, with nightime temps no lower than 53 F is best for flowering.
If it gets too hot they either shant flower or will experience flower drop - too cold and you'll also get flower drop followed by dormancy. The indoor grow room, should be manipulated to give the dry warmth of summer to induce growth, followed by damp and cooler conditions to induce flowering..
14 - 16 hours of light daily is the optimal day length to induce flowering. Post flowering the day length can be reduced to 12 - 14 hours.
Flower bloom, under the proper conditions, generally occurs within 2 -3 weeks after planting. Once the flowers emerge, they open fully in roughly 3 days - once open they are ready for harvest.
Plants that grow via Bulbs or corms, do best with lots of phosphorous and potassium for growth and flower production. Not too much nitrogen, just a modest amount. Hydroponic nutrients are not absolutely essential for germination, if you choose this route, the corms/seeds should be supplied with nutrients mixed at less than half strength.
Some of the more adventurous growers like to delve into plant chemistry and concoct their own nutrient solutions. This can work out just fine, assuming you are willing to deal with some plant losses while experimenting, and are able to calculate all the variables that can lead to over nuteing and nutrient deficiencies. Personally - I fell there are too many other facets of hydroponic gardening to devote my brain cells to.
In the case of Saffron Crocus, the only thing you are interested in is germination and flowering. Once the plant has flowered it is no longer of any use, the stigmas are harvested upon bloom.
This being said your nutrient solution should be one designed to promote flowering / blooms and enhance their essential oils which produces the flavor. All other variables such as pH balance, Secondary and Micro Nutrients and so forth should be the job of the professionals who formulate the solutions. See Nutrient Solutions to Promote Blooming.
Any nutrient solution should contain all the necessary elements: N, P, K, Ca, S, Mg, Fe, Mn, Zn, B, Cu, Mo but with higher concentration of Phosphorous and Potassium. This is basically how bloom formulas are based. Dilution as per manufacturers instructions.
Nutrient values can be measured periodically with EC meters. EC is Electrical conductivity, EC as well as TDS [Total Dissolved Salts] are used to help determine the strength of a hydroponic nutrient solution. Nutrient ions [Salts, minerals, metals] have an electrical charge, a whole number, usually a positive or negative 1, 2, or 3. EC is a measurement of all those particles in the solution that conduct electricity.
There are no meters that will indicate what elements are in your solution, or in what quantity.
They can't even tell you if the elements within the parts per Million are useful or harmful elements to your plant. For a nutrient solution to do it's intended job , all the mineral elements within it need to be in balance. See - TDS in Hydroponics
To harvest, pick the flowers as they open. Inside the flower will be 3 , sometimes only 2 deep magenta colored stigmas which is what you want to harvest. It is dried and becomes Saffron Spice. Do not confuse other flower parts with the red gold that is the stigma - the rest of the flower is useless from a culinary point of view.
You will probably notice that the deep red strands / stigmas are very fragile - they would blow away with the slightest breeze and they frequently do. Electric dehydrators or even sun drying them does not do justice and frequently leads to disappointment. The best way to dry them is to allow the air to dry them naturally, remember now - a slight breeze and they're gone. I like to dry mine on a simple sheet of paper in a dry location away from any fans or open windows. It should take about a week to completely dry at which point you can store it in airtight containers. If not stored properly and moisture reaches it, mold and fungus is a real possibility.
Footnotes - References
1. The world's priciest foods CNN Money
2. BULBOUS FLOWER PRODUCTION SYSTEMS: STATE OF THE ART Academia.edu