When I was in Arkansas, about the same latitude as Tennessee, I'd set the onion and garlic bulbs in the fall, two or three weeks before the first frost. They'd set roots and be ready to take off as soon as spring hit. Most years I'd mulch them a little but nothing extravagant. Some years I'd plant them about now and they'd do OK but I preferred starting them in the fall.
I'd get those bunches from a local Mom 'n Pop gardening store, often not much of a selection for variety but the best price around. They may say 50 per bunch but most I got had closer to 70 sets. When they gathered then they just grabbed a handful, never counted them.
Here in Louisiana I have the same issues you do with Bonnie Plants. Everybody seems to get their plants from Bonnie. So they all have the same thing and the same shortages. Some things they don't even mark what variety they are, just call them Cauliflower or Broccoli. Frustrating.
With the pandemic a lot of people are getting into growing stuff. That has totally disrupted the supply chain, it can be challenging to get seeds mailed to you let alone find starts. Many mail-order sites are out of seeds.
I don't know where in Tennessee you are but look around for a co-op. I've had some luck with those. And look online for a mom 'n pop type place, not a big box store. The big chains are all probably ties to Bonnie or the equivalent.
Good luck with it.