how do I determine which one to use for any given router bit?
You don't need a bushing at all unless you're using some sort of template to guide the cut. When you do use one, choose the size of the bushing according to the offset you want between the template and the cutter. Your choice will therefore depend on the template or jig that's guiding the router, and the result you want.
Do I want the tightest tolerance possible?
No, not necessarily. Again, the bushing determines the offset from the template. It would be entirely reasonable to use a 1/4" bit with a 1" OD bushing.
In some cases, the bushing might actually be smaller than the cutter diameter; that's very common with some dovetail jigs, e.g. the Leigh jig. Obviously, you can't use a bit larger than the bushing's inside diameter if you need to make a plunge cut. And if you want zero offset between template and cutter, you're usually better off using a bit with a bearing, like a pattern bit or flush cut bit.
If I'm using a dovetail bit, how do I determine what's the right size? Does the bushing just need to clear the shank of the bit?
If you're using a dovetail bit with a jig to cut dovetails, the manual for the jig should tell you what size bushing to use for a given bit. Different jigs have different capabilities: some only do half-blind dovetails, some do through dovetails with fixed spacing, some can do through dovetails with variable spacing. At least until you really get comfortable with whatever jig you're using, it's best to stick to the combinations recommended in the manual.
confirm order
, so I don't have it to hand quite yet to even try things out.