It is easy to grow. Just stick the bulb about 1" to 1.5" (25 mm - 40 mm) below the surface and water it in. Keep it moist but not wet so the bulbs don't rot. It will sprout and then produce a nice flower which will have the red stigma or styles that you seek. Each flower will have 3 of them. They pluck easily and take about a day to dry naturally.
Insects will visit the flowers like any other flowers. You have a time-limited window in which to pick them before the flower dries out and it becomes more difficult to separate them from the petals by hand.
The part of saffron growing that makes it expensive is the labor involved in harvesting the red bits which give the distinctive flavor. All of this is done by hand and if you have lots of crocuses to harvest from then you will spend a lot of time gathering them.
We have a couple of 2' x 4' (0.6 X 1.2 m) galvanized steel oval raised garden beds where we grow ours. They are filled with high quality raised bed soil and we do not fertilize our garden except with mulches and compost.
We had a great showing during the hottest part of the summer last year. In total we were able get several grams of saffron from our two raised beds which have between 75 and 200 plants growing in them. I don't really have an accurate count of the number of bulbs we have.
EDIT: This photo shows the saffron beds in our garden. [0] We are still in the process of clearing things this spring. Inside the rings you can see our bulbs, truly a tiny fraction of a metric fuck-tons worth but they have so far yielded several meals worth of flavor. We use about a dozen threads per meal which means that 4 blooms will give you enough for a single meal.
[0] https://postimg.cc/pmJbhZVk
EDIT2: I may have implied that a small operation like ours still takes a lot of time to harvest. That is not accurate at all. Since ours are confined to those two beds and considering that they don't all bloom at once it is a simple process to collect the saffron once the bloom period begins. It takes us a few minutes a day and we spend that time out in the garden anyway managing our other things so it really requires no extra effort to grow and enjoy this spice.
[0] https://www.rareseeds.com/crocus-saffron-25-bulbs
We have also bought from an online seller through Amazon and had similar results with the bulbs we planted. After our success, several relatives have also bought saffron crocus through BCHS or an Amazon link and will be having their first harvest this growing season. There are some Amazon sellers who still have some available. [1] It will also be pretty widely available in the fall from other heirloom and organic seed and vegetable sources since it is typically planted in fall so it can over-winter outside.
For us it did not matter that we added to our plantings in the spring last year. We had an unusual cold snap that kicked them into gear and the summer was hot and dry. It was great.
[1] https://www.amazon.com/saffron-crocus/s?k=saffron+crocus
The next year two of my three locations came back with strong leaves and offshoots, but almost nothing flowered. A big disappointment. This year I'll split them up (or maybe split up just one bed) and see what happens. Despite this, I'd encourage anyone in the right climate to give it a shot.
Also, if you're looking for easy expensive spices to grow, try bread (opium) poppy.
Someone else commented that the claim of having to harvest in early morning is silly-- can confirm; just pick them whenever is convenient, but the flowers do only last a couple/few days. Also, no need to harvest the entire flower, just pull the stigmas with your fingers (it isn't difficult, just time consuming).