These two black holes wouldn't stick to each other, but start swirling around each other and eventually merge together.
This is partly because of friction with and among other stuff in orbit around the black holes in their "accretion disks". (Black holes experience friction by eating the stuff in the other hole's disk of debris, with the momentum of the black-hole-plus-dinner thus being different from the black-hole-before-dinner.)
It's also partly because the rapid acceleration of things passing near a black hole or orbiting it causes the emission of gravity waves to be strong enough that it carries off substantial energy. (In less extreme environments, like suns and planets, the waves are not detectable by current instruments. In the case of two black holes,orbiting each other, they're detectable from across pretty much the whole universe.) This loss of energy amounts to "friction" that eventually causes co-orbiting pairs of black holes to spiral in and combine.