2006 harley street bobber. My transmission jumps when I hit a bump

Most likely some wire in harness is worn and grounding when you hit the bump, check harness under tank first, lots of pressure there pressing wires against frame. Especially if you have had the plastics off or the tank off recently...

Isn't it still under warranty?

Have the dealership take a look at it.

the battery needs to be replaced, the alt can't charge it and try to keep the bike running at the same time when the battery is bad,

Wonder about your stoplight, taillight? Most of that stuff runs off the accessories fuse. Check that fuse to see if it is blown. If it is, replace it and see what happens. If it blows immediatly, you've got a dead short somewhere. If it stays there, you may have an intermittent short. The intermittant short is a bear to find because it's tough to fix a problem when it ain't there. Electrical problems are always difficult and this about the best information I can give you. It's a starting point.

Good Luck
Steve

would guess that they are not bottoming out, they are topping out. doubt that you get them to full compression on bumps or braking would really be a bad experience, it's more likely that after compression on a bump, the forks spring back out as far as they will go and reach the end of their travel, it's because they aren't very sporty forks and lack enough rebound damping. I have a 2008 1200 sportster and it does it. cure would be maybe thicker oil in forks to slow up the rebound but would also slow the up stroke over bumps. you can get just about evey accessory for a Harley so there's probably a kit available to fix the damping.