EDIT: You can probably ignore what I said originally, as I just thought of a much better way - will leave my original post intact just in case.
Try running the following from the command line:
mame -verifyroms romname
where romname is the game in question. If you're missing roms, it will list them and the name of the set they belong to will be listed in brackets at the end. That'll tell you which bios you need.
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ORIGINAL POST:
Try running the following from the command line in your mame folder:
mame -listxml romname
For example, if you try mame -listxml mslug, dig through the text it outputs, and you'll find
romof="neogeo"
indicating it requires the neogeo rom to run. Alternatively, if you do this
mame -listxml mslug > mslugInfo.txt
it'll output the text to mslugInfo.txt and be a little easier to search through. Also, you could try
mame -listxml > mame.xml
and then have the xml info for all the games and search through it that way.
I feel like there should be an easier way, but a quick look through the mame docs and a google search turns up nothing.

Hope this helps.
