Well, I also like to finish what I'm turning in the same day if possible.
The drying times depends on more on what type of finish you are after for example, if you like a thin oil finish with a matt or low sheen, you can use one of many timbers oils that you apply while on the lathe as they always require "burnishing", if you want a very gloss finish and your woods are some how a little porous, you require one good soaking coat of thin sanding sealer and then one or 2 costs of the top finish/varnish, this can be done in a couple of days depending on what temperatures you have in your working areas.
You can use one of the satin type quick set/dry spray cans and have the piece coated and ready to put away/stored dry in a couple of yours or less, these I use often when I just want a simple and fast finish. An example of this is a simple 13" platter I turned and finished yesterday afternoon, I gave it 2 light coats and was handling it, in less than 45 minutes, see attached.
These cheap spray cans were purchased at the "reject shop" in a town next door a couple of years ago, I was very impressed with it so I purchased all they had, unfortunately, I used the very last bit I had in my last can on this piece, I want more of it but, they no longer sell it
Hope this info helps you...!
Cheers
George