This question reminds me of a germaphobic classmate I had back in Middle-school. He would always stay clear of public lavatories/urinals because he was under the impression that urinating at one would result in bacteria from the urinal climbing up the stream of urine and into his urethra...needless to say, he was a very lonely boy.
The situation you described ("Drinking without sipping") is a modification (albeit, a more reasonable one) of the "Bacteria-climbing-up-a-stream-of-urine" theory.
I'm not a chemist myself, and like you, I am faced with... ahem, "issues", while searching for speeds of common ions in water (at a given temperature, and in the absence of an external electric field). But I feel this question can still be satisfactorily approached even without these values.
From the wording of your question, I suppose you assumed that potassium, sodium, magnesium and other ions would diffuse from a region of higher concentration (the saliva in your mouth) to a region of lower concentration of those ions (the stream of water entering your mouth). Now this would seem perfectly plausible if it weren't for a few things:
1) You're dealing with flowing water
This isn't a simple case of spitting into a glass of water and waiting for the contents of your saliva to (passively) diffuse into the water (and eventually form a dilute saliva solution). By drinking it the way you do, the passive diffusion of electrolytes in your saliva won't be able to match the speed of the water flowing into your mouth, much less exceed it in order to enter the bottle.
2) All the electrolytes in your mouth are trapped in a viscous protein-soup
Human saliva contains a variety of proteins (among other things). Common experience tells us that saliva is (a little more) viscous than water, and doesn't "instantly" dissolve in it (<----- Coming from a guy who had to spit in test tubes for his Biology lab assignments). Now not only do the electrolytes have to actively diffuse upstream to get into the bottle, but they also have to "free" themselves from the saliva first.
3) What do you mean by "saliva"?
This is the philosophically inclined conclusion to my answer. You're worried that the entry of electrolytes from your mouth into the bottle (won't happen) counts as contaminating it with your saliva. At first glance, even if the electrolytes seem to be able to make it to the bottle, you're pretty sure that larger molecules (such as proteins) won't be able to do the same.
If you don't count the proteins, epithelial cells and bacteria that normally constitute human saliva...how would this make saliva any different from a simple laboratory-prepared cocktail of sodium, potassium, magnesium, calcium, etc? Besides, ordinary (un-branded) bottled water would already contain these electrolytes; so by that logic, the water's already contaminated with your "saliva" even before you opened it!