There's many posts about this on the production forum on TA. However, a lot of producers would suggest you indeed do group your kick and bass and compress them together, so they work together nicely.

However to do this, you still need to make sure your kick is always prominent and doesn't get drowned out by the bass during compression. Achieve that by a few ways - not playing the bass when the kick plays; lowering the bass when the kick plays; EQing the bass and kick so they don't clash etc.

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Monsoon - Astrosurf

You can compress the bass if you want. Compressing the bass can give you a nice punchier sound too. When you compress the kick/bass together just make sure that you have a small ratio so that neither instrument gets too much reduction.