Here is my list, like the others you will see that it is pretty basic.
- Bandsaw, being able to rough out a stave in 10 minutes is a real treat, however if i didn't have a bandsaw a nice sharp broad axe (that is one that is flat on one side) would suffice.
- drawknife, can't be without a couple, one dull for chasing a ring, one sharp for actual cutting.
- spokeshave, quickly becoming my favorite bow building tool, love it, love it, love it.
- ferriers rasp, i use my cheap ferriers rasp more than i use my expensive rasps because i can't hog off wood with #50 without it plugging up on me.
- Nicholson 49 or 50 or UBR10, unmatchable performance when more controlled wood removal is needed.
- card scrapers, the one and only tool for final tillering as far as i'm concerned.
If you omit the bandsaw and expensive file i'd image you could pick up the other tools: hatchet, drawknife, spokeshave, ferriers rasp, and card scraper for about 50 bucks if you got some from 2nd hand stores, flea markets etc.
you don't need a lot of tools to make really good bows, just search "hatchet bow" and see what people have done with only one simple tool.