If a provider has HSV-1 (the herpes variant that causes cold sores), you can get genital herpes from BBBJ if you don't already have HSV-1. About half of all genital herpes infections are HSV-1 through oral sex. However, more than half the population already has HSV-1. If you already have it, you can't catch it again. You can get infected even if there is no visible cold sore. With a cold sore, the risk of infection is almost 100%, but even without a cold sore there is virus present about 20% of days.
Risk for the other STDs is minimal from BBBJ.
You can get a vaccination for Hepatitis A and Hepatitis B, and HPV, and anyone involved in this hobby probably should. Hepatitis is not typically transmitted through BBBJ, but rather through sex, but it is incurable and there's no reason not the get vaccinated.