What is the Ph of your water? I have a book that I could also highly recommend to anyone on the board who is interested -
Manual of Fish Health
Dr. Chris Andrews, Adrian Exell & Dr Neville Carrington
Anyways, It has pictures of every disease that is in it and its a pretty weighty book as far as fish books go so it really helps to identify diseases. I looked up blood in fins and betta's and one main cause of blood in the fins is from either acidosis or alkalosis. Many people will say that fish can adjust to the ph that you put them in and in some instances that simply is not true. Here is a quote from the book on this -
"The behavioural and physiological symptoms involved in alkalosis are much the same as acidosis. In addition, the fish's gill and fin tissues are destroyed. A further problem experienced at high pH levels is increased toxicity of ammonia,"
Betta's a fairly tolerant species. However, I have seen alot of debate about how for say, discus, can be kept at any pH. I just wanted to take this moment to say that all fish have a range of pH for which their body functions properly and if not kept in the right RANGES of pH, the toxicity to things in the water is so much worse for them. Anyways, I will stop because I am sure this will spark some debate.