a little bleeding is normal from your bikini line because of the thickness of hairs and sensitivity of the area, as you repeat it will lesson, it just takes time.
some tricks to minimize the pain- take an analgesic about forty five mins before,
make sure you are holding the skin very tight
you said you were having to do multiple applications that should be mostly unnecessary so make sure you are applying the wax firmly so it goes all the way to the skin and press the strip firmly,down, with the nair wax it actually helps to rub it into place and pull parallel to the skin
the faster you pull the less it hurts
I dont have expierence with bikini zone but generaly I recomeend that you leave the skin alone as much as possible during the first 24hours,
For the bumps I recently read a post from ashley bush that suggested that 24-48 hours after waxing you start to use stridex pads, 2 or 3 times a day on the area
good luck next time
autum