What could cause bloody discharge with otitis externa?

Invasive infection: It could either due to era drum rupture of invasive bacterial infection like from pseudomonas. Need to see a doctor.

Infection: Most often bleeding is a result of granulation tissue or extremely swollen tissue that readily bleeds if touched by fingers or qtips. The steroid component of ear drops helps with this. I assume you are seeing a doctor and are being treated... If not you need to! if there's a lot of bleeding, in the short term you could try a squirt of otc oxymetazoline which can shrink tiny bleeding vessels.