Can one get infected by a sexually transmitted disease if one ingests bodily fluids from an infected person?

Yes.... sort of. Oral sex is one way to pass std. Herpes, hpv and syphilis are passed by mouth to skin contact. Gonorrhea, chlamydia and HIV are examples of disease passed by fluids. Ingesting the fluid though is not the issue. The fluid coming into contact with the tissue of the mouth and throat are how infections occur.
Very unlikely. If the "bodily fluid" in question is semen or other sexual secretions (e.g. cervical-vaginal fluid), there could be risk of gonorrhea or other STDs. No other "bodily fluid" is risky for STDs, and that includes blood. For example, oral exposure to HIV -- even infected blood -- rarely result in infection.

Related Questions

Is it possible to get eye herpes or other sexually transmitted disease from getting infected semen in your eye?

Yes...sort of. Herpes, hpv and syphilis are passed by skin to skin contact not from fluid transmission. Passing these diseases in the way you describe is unlikely. Other diseases like gonorrhea, chlamydia and HIV are passed via fluid transmission from one person to another. Mucous membranes around the eye can become infected. In fact, chlamydia is a common cause of infant blindness acquired during delivery. Read more...
Yes. Although to my knowledge that study has never been performed. It would seem likely that exposure of a mucous membrane such as the eye to infected semen could result in transmission of disease. Read more...