That photo doesn't look like it's been cut on, is that the right one? No to the rubber band, no to the DIY amputation (you can't anesthetize a bird properly for surgery without training, they have a completely different respiratory/metabolic system than mammals). Yes to what
@azygous said. The vet should have given you some instruction on cleaning and treating it, but if not....
I had a rooster's toe amputated by my bird vet of 30+ years last month, it had done just as azygous said and turned black. My fear was that it would creep up into the foot more so I went to the vet (I need this rooster's genetics). $210 later and he's five-toe McGee. It was the same toe as yours, but worse. Instructions were to take off the vet wrap after 48 hours, wash it gently in running water, and put Silvadene cream on it. Monitor it to make sure the wound doesn't open, and let him be a chicken. Like I said that was last month. It swelled up worse than it was originally and looks awful, but there's no infection and no necrotic tissue, so he gets it cleaned every other day and I have to watch his breastbone for blistering due to laying down all the time. After a week or so he started to stand and now gets up and stomps around like an elephant to get to his food. He started crowing again after about a week too. Granted, I don't have him in a cage big enough to wander around in, but he can walk 3-4 steps across for food and such. I'm still in the monitoring phase because there's still a lot of swelling, but he's not in pain when he moves around or I clean it, so I'm doing the time heals all wounds thing for now.
I did have one a while back that ripped a nail off and the last knuckle of the toe turned black and self amputated. It was a slightly unsettling process, but I can attest that it does happen and they don't seem to be bothered by it. Make sure to treat the bumble foot properly, but let the rest of the foot do its own thing.
Well crap then. Clean it, treat it with Silvadene or antibiotic ointment and let it crust over, you might wrap it for a day or so. Non-stick pad, gause over top, vet wrap over that, not too tight. If you feel fever in it, it smells, or there's pus or other signs of nasty infection, find an avian vet in your area or call the local zoo and ask their vet's advice.