You do not need to use a dryer with rollersets, just airdry. However, reason a hard bonnet dryer is a good thing to have if plan on doing rollersets as part of a regular routine is because will speeds up the drying time. I have 4b hair and my rollersets dry as follows:
airdry - 7 hours
hooded dryer on cool - 3.5 hours
hooded dyer on warm - 2 hours
hooded dryer on medium - 1.5 hours
hooded dryer on hot - 1 hour
I have elminated heat by drying on cool only. I just don't have time to airdry each time I wash, although I do airdry every now and then, like on slow weekends around the house. . .
Sponge rollers (satin cover or not) will make your hair super curly with tight curls rather than smooth and bouncy. IMO, the best sets are when you use MAGNETIC ROLLERS, any BSS, sally's walmart will have these. I started out 5 years ago when my hair was very short using the yellow ones and slowly worked my way up to the larger red and purples ones. You should be looking for roller size based on your hair length and get the largest diameter your hair will take -- thus results will be smooth, loose curls rather than tight curls. The smaller the rollers, the tighter the curls and less bounce (I learned this the HARD way early on). If you've never done rollersets before, I strongly recommended having a professional wash and set and then pay attention and ask questions -- rollersetting is a skill to be learn with much practice --it is not as easy as it appears (I learned this the HARD way too!).