Can prostatitis result in bloody semen?

Sometimes. Semen is produced in the prostate and is expelled when you ejaculate. Prostate infection causes inflammation and pain can occur in the prostate, penis, testicles and pelvis. The prostate is most active during arousal / ejac and penis pain is common. Color, volume and consistency of the semen can change. See an md for possible antibiotics. Other causes include: urethral scar, urine infx, stis.
Yes. Bloody semen or bloody urine are not unusual in patients with acute prostatitis but there other conditions that can cause this as well.