I've been learning to play the harmonica for a couple of months now (on and off, honestly), and whenever I switch to different notes there's this soft popping/bubbly sound because of the saliva--how do I stop this from happening? It's loud enough for others to hear
If it is saliva, you need to find ways of reducing that - not only does it contribute to the popping noise, it also won’t be doing the reeds of your harmonica any good. How you do that will vary person to person, but watch what you eat & drink before playing.
It may also be that you’re pressing too hard on the harmonica; you need to seal the lips to prevent air loss, but you don’t need to clamp the instrument to your mouth.
If you are playing a chromatic harmonica (= with a button on the side), then the most common source of popping are the wind savers (valves) getting wet from condensated breath. The remedy is to have the instrument at body temperature before you start to play (eg have it in your pocket for 15min).