It is normal to have a little saliva in your mouth while playing, but it shouldn't be to the point where you are blowing bubbles. The excess saliva could cause the reeds in the harmonica to stick.
Make sure your tongue is completely relaxed while playing. I've noticed that the production of saliva in my mouth increases if my tongue is not completely relaxed.
You could also try tilting your head (and the harmonica) UP a little, say to a 30 degree angle. This would keep the saliva in your mouth from entering your harmonica.
I experienced this problem when I started playing. It usually takes a few days (or weeks) before the muscles in your mouth understand how to reduce the production of saliva.