Sandpaper?!? Gerard, I'm shocked.
You're gonna get me started on a rant here Jake. Yes, sandpaper. I don't know what you're seeing in your shop or the L&McQ shop, but most - as in 90% or more - of the bridges I get on my workbench have hollowed-out feet. Carved with knife or very shallow sweep gouge, these bridge feet, whether it's on a violin or a doublebass, are making less than 50% contact with the tops they're 'fitted' to. Often it's less than 30%, whether it's a bass just off the boat from China or from one of the local shops with a luthier-branded bridge for which the player has been charged hundreds of dollars.
Carving a bridge foot is all well and good for the very few craftspeople capable of such precise work, but those are about the same proportion of luthiers who are capable of accurately fitting an oval inlaid soundpost patch or a through-patch. As in a very, very small group. In the Weisshar-Shipman book they suggest that such work (a belly through-patch) "is a sophisticated repair technique and should be undertaken only by experienced restorers!" Fitting a bridge isn't so rarified, and the absolute accuracy of fitting isn't no glaringly necessary, but if a bridge doesn't fit well (90% wood-to-varnish contact or better) there are two problems: discontiguity makes for inefficient transfer of vibration, and damage to the varnish and eventually the wood of the belly is inevitable as the high points dig in.
So yes, I fit bridge feet with sandpaper. 100x Norton 'World's Best Sandpaper' for rough fitting, then 220x, same brand, for finish shaping, then a careful swipe or two with a flat knife blade and/or a fine file to remove any fuzz left on the surface. A very close fit is quite easily made with this method, with pre-fitted adjusters (it's a bit more complicated with a fixed-footed bridge, owing to the need to pre-stress the legs simulating strung-up leg spreading, and the increased awkwardness in sanding two feet at once) provided one follows a few basic rules:
- Clean the sandpaper back carefully so as not to scratch the belly or leave bumps of grit which interfere with fitting.
- Clean the belly just the same.
- Hold the sandpaper such that there is absolutely no chance of it slipping.
- Sand in a motion parallel to the bridge (this is with a bass - with the smaller instruments a jig is more accurate and practical).
- Move the bridge foot in a pattern initially about 1/2 the length of the foot, reducing this motion as one approaches a decent fit to no more than 1/4" of motion. Excessive following of the arching will lead to a rounded-over foot which doesn't fit well at all.
I'm not going to name names here... but will say that I have improved the fit of many a bass bridge with this method. Of course I've been doing it for over 20 years, it'll be harder for the guy asking this question to do it for the first time. But he's determined to save some $$$, sounds interested in doing the work, so what's the harm? At worst he ruins a cheap bridge blank and then saves up and takes his bass to a luthier to have it done well (or not, depending on the luthier's attitude). I wish more players would take the initiative and do external fitting stuff for themselves. Especially learning to fit a soundpost. Seems to me pretty much every touring bassist should take lessons in soundpost fitting. It'd save virtually infinite grief to instruments, as posts could simply be taken out for flights then popped back in at destinations in a couple of minutes. Instead we see countless unnecessarily wounded bellies and backs, posts sometimes poking right through. Good for luthiers wanting to make money, bad for instruments, musicians, and ultimately music, as a soundpost patch will never quite render the same sound as the original instrument. Close if done well, but not quite the same.
Anyway, best of luck fitting the parts. Loads of music teachers used to do this sort of work, some still do. There have even been books published specifically for music teachers repairing instruments, including instructions on making bridge fitting jigs. Can't remember any titles, but a visit to a library can be most illuminating.