Why is the BPM of bass drums divided by 4? In other words, if someone hits the bass drum 1200 times in a minute, it is considered 300 BPM. Why is this?

if he's playing 16th notes, then he would be playing 4 times for every beat

It's due to how the notes, or drum hits divide the measure. For 16th notes there are 16 notes in a 4 beat measure. So you would divide the number of drum hits by 4, since there are 4 hits per 1 beat. If the drummer is playing 8th notes there are 2 notes per 1 beat and therefore you divide number of drum hits by 2. It's an easy formula to understand once you learn how the various types of notes, whole, half, qualter, eigth, sixteenth, etc. divide the measure.

Makes sense, I just dont really understand drum notation very well.

It's not really just drum notation but notation for all instruments. I learned how to read sheet music in middle school when I was learning Saxophone, so the math behind music is a bit easier for me to understand. In contrast; someone whom has not learned how to read sheet music might find this concept hard. Why are you concerned with BPM measurement if I can ask?

I think you're confusing beats with bass drum hits. The timing and speed of the bass drum hits does not determine the tempo. If the tempo is 240bpm (4 beats per second) and the drummer kicks on every beat, he will kick 240 times per minute. If he kicks 4 times every beat, he will kick 960 times per minute. Even though he's kicking that much, the tempo is still 240bpm.

Tempo is, as a musical term, merely a question of notation. Theoretically speaking an incredibly fast song could have a very slow tempo, and vice versa.