According to CDC, any HIV test is conclusive if taken 12 weeks after an exposure, but you can take them before that, 3rd gen will give you an excellent indicator about your status around 6 - 8 weeks after exposure and 4th gen 4 - 6 weeks after exposure. A result given in those times is very unlike to change, but only a doctor, based on your risk level and his experience could advice you to skip the confirmatory test after 12 weeks post exposure.
Bleeding gums and small cuts doesn't make any difference unless they bleeding is profuse.
Your risk would depend on what kind of sex event you had, if was vaginal, on average your risk would be 1 in 2000 only if your partner was HIV+.
Hope this helps.