I don't know anything about whether you should buy bulbs or not as these knowledgable people above clearly do but I used to have snowdrops in my old garden - in the ground.
I suspect it depends on the region but I live in Sussex and mine used to start in Jan or at the latest early February. A tiny little green stump/shoot would appear which would get taller and taller and the leaves appear by kind of "peeling away" from the stump until suddenly a flower appears!
If you are going to keep them in the pot year after year I did see on TV once that sometimes you have to divide them (like every few years) by waiting until they have stopped flowering and digging up a clump and splitting it into littler clumps and planting them elsewhere (or giving away or whatever)but I'm not sure if this applies when they are in a pot. I know that if you don't divide daffodils they stop flowering but I'm not sure if its the same with snowdrops or if you just divide them as a way to propagate.
Also, if it is of interest, they were very tough - my daughter stomps all over the stumps EVERY year (usually because it has snowed ) and they always survive!