This idiom 'run with the hare and hunt with the hound' means figuratively to support both sides of a dispute. Here it refers to 2 persons or parties, but it could also refer in other contexts to supporting 2 competing sides in an argument. The idiom shows how difficult and quite impossible it is to do both at the same time, since literally you can't be on both sides hunting the hound and running with the hare.

there is a perfect Russian saying - "if you chase two hares, you won't catch any of them" or the modern variation "If you chase two hares, they cooperate and hit you on your snout" also "you can not expect to climb up a fir-tree and not to scratch your ass" ))))

'Hare' and 'hounds' refer to two persons or two groups of people with whom Bob is not on good terms. In fact, 'run with the hare and hunt with the hounds' means to have a friendly relationship with both sides. Maybe Bob couldn't get on with both sides because Bob and the others don't share the same opinions or beliefs or maybe they have different characters.