Interesting question & you are right, blood is one of the body fluids that can transmit HIV.
It is perfectly okay for consenting individuals to have sex during their menstrual cycle. Whether the individual is menstruating or not, condomless vaginal sex, can be a risk factor for passing on sexually transmitted and blood borne infections (STBBIs) like chlamydia, gonorrhea, hep B, herpes, HPV, syphilis including HIV. Using a condom (internal / external) will lessen the risk of STBBI transmission.
If the HIV positive individual is on anti-retro viral treatment and their viral load is suppressed (undetectable) then the risk of transmission is eliminated. If not on anti-retro viral treatment or their viral load is detectable, wearing a condom or using a sex dam (or a cut condom) for oral sex is recommended.
