accidentally drank someone water bottle?

Unless they are very ill. You will be good.

Its a nice thing we humans have called an immune system.

down toilet?

How do you get rid of what?? the other persons germs?? Too late, the instant they hit your mouth, you got them in your system..

let me ask you this: do you also freak out when you kiss your significant other? Or do you sterilize their mouth first??

The water you drank will pass just like any other water.

It will not be identifiable as "water from someone else's water bottle"

I am sure through your life time you have ingested plenty of things from someone else's plate, bowl, spoon, glass and you have suffered no ill or strange side effects to this point so I am guessing the same will hold true here.There are plenty of other things to worry about in life, if this is the most worrisome thing you have to ponder consider yourself a very lucky person.

With pizazz! Stand up and loudly proclaim "I AM AN IDIOT FOR DRINKING FROM [friend's] WATER BOTTLE AND I APOLOGIZE PROFUSELY!" Then strut across the room and get a replacement. Proudly return from your quest, and with a deep bow, maybe even a knee, present the new bottle as if it was a gift to royalty.