How to make 9V battery clip easier to work with breadboard
You could solder the ends onto some stiff wire pieces or (better)  onto a 0.1" (2.54mm) pitch header (pull out some pins if you want more spacing than 0.1"). 

Put some shrink wrap around each wire if you really want to do a nice job. Source here. Naturally you'll need to thread the heatshrink tubing on before soldering, then slide it down and shrink it into place. 



By the way, usually the back of those solderless breadboards can be peeled back or otherwise removed and the errant piece of wire cleaned out.