I've got an intermediate screw base light bulb that I want to replace (as it's burned out). However, going around to local stores they only have the correct size & wattage of bulb available in either medium base screw or some weird looking 2 prong thing that I've never seen before. Since adapting medium down to intermediate would probably take up too much space, are there 2 prong to intermediate base adapters available anywhere?
Yes they are definitely available though specifics as to where to buy them are generally considered off-topic for this site.
Here's a GU10-WHIP flexible socket adapter:
Or here's a more traditional Bi-Pin to Standard Base adapter:
You may be looking for GU24 bulbs
Relevant question: Are standard light bulb bases being phased out?
If so, a typical Edison Screw Bulb may work fine but you're better off buying the bulb intended for the ballast.