There shouldn't be any life forms in the central bulge of the galaxy as there are very little amounts of the heavy elements in the central bulge which are necessary to form planets and as far as we know, life.
The stars in the central bulge are much closer together than they are in the disc (where we are) and the spirals, so planets that have formed there could have had their orbits easily disrupted by a passing star, causing them to spiral into or away from the sun, so there would be very little chance of life survining, if it did manage to form in the first place.
The average distance between stars across the entire galaxy can be calculated by finding the stars per unit volume and cube rooting, which would give about 3.5-4.3 light years, however this would vary across the galaxy, it would be greater than this near the galaxy's edge and would fall as you move towards the central bulge. I can't find any figure at the moment though.