In humans, Ureaplasma may be transmitted by direct contact between hosts (i.e., through genital-to-genital or oral-to-genital contact).

Ureaplasma urealyticum can cause urethritis (inflammation of the urethra) in men. 

However, Ureaplasma species have been isolated from specimens taken from the cervix/vagina in 40-80% of women who are asymptomatic and sexually active.

If your girlfriend is simply a carrier of the bacteria, meaning she does not have active symptoms, and as long as you do not have symptoms of urethritis such as burning, pain, interrupted urine stream, urinary frequency, then you need not worry. As a measure of precaution, however, it is advisable that you do a urine analysis and culture to see if you too carry the bacteria, just in case you end up developing any urinary symptoms.