You had NO RISK for HIV and do NOT need to test. This is NOT how HIV is contracted.
What if they had bleeding gums?
STILL NO RISK
The 3 ways you can contract HIV
1) UNPROTECTED INSERTIVE ANAL/VAGINAL SEX WITH HIV+ PARTNER
2) SHARING IV DRUG WORKS (NEEDLES) WITH AN HIV+ PERSON
3) HIV+ WOMAN TO HER UNBORN CHILD
Absolutely none!
Even IF the water in the bottle contained HIV+ blood, the time the virus had been outside the human body would have rendered it inactive. There is also air in the water bottle which would also render the virus inactive. There are bacteria and enzymes in YOUR saliva that would render the virus inactive. And as I've already pointed out, this is just NOT how HIV is contracted. I have outlined for you the three ways you can contract HIV. Drinking from an HIV+ persons water bottle is NOT on that list for a reason.
You never had a risk for HIV and you certainly do not need to test. What you DO need to do is educate yourself about HIV so your anxiety is brought under control.
BTW..........does your gym have a pool or a Jacuzzi?