Q:

Can I ignore the bottom number in a time signature if I know the BPM?

I never remember what that bottom number means, can I just stick to the top number and call it a day?
So in a 6/8 I could just know that it's 6 beats per measure (ignoring the 8).
If I know my BPM (for example 80 bpm), then does the top number suffice?

A:

No. For a start, there aren't six beats in a 6/8 bar. There are two, each beat lasting three quavers. Think 1 2 3 4 5 6. The beats are on 1 and 4. This is called a compound time signature. 
The concept of beats per minute is a little hazy because of this. Digital Audio Workstations can make this even more confusing, because they often falsely equate beats per minute with crotchets per minute. That's fine in 4/4, but wrong in many other time signatures. 
So to use a BPM marking (or, more generically, a tempo marking), you need to understand what a beat is in a particular time signature. And to do that you need both numbers. It tells you the number and type of notes in the bar, and also the emphasis or grouping of those notes.
Could you muddle along without knowing all this? Probably. But you'll end up with weirdness somewhere down the track (using a DAW in 12/8, for example), and it would be easier to fix if you understand a bit more of what's going on. 

