Use a mastitis prep such as Tomorrow and use it topically. The tip of the syringe gets the medicine in where you need it, it won't hurt the horse or you, it's thick - stays where you put it, it's cheap, but most of all, it works and works FAST.
IF you decide to use bleach, a bleach/water mix, lysol, ect. Don't put it in a spray bottle and spray it on as it can splash back into your face…use a sponge and wring it in where you want it instead. You just don't have the control with a spray that you do with a sponge.