The visitors came close midway through the first half as Ivan Sproule jinked into the box from the right and curled in a shot with the outside of his foot that went just wide from ten yards.
They went closer minutes later as the ball fell to McAllister on the edge of the box and the Robins left-back fired in an arrowed shot that looked destined for the top corner, but keeper Boaz Myhill was more than equal to it as he stretched to turn the ball round the post for a corner.
Gary Johnson's men came close again in the latter stages of the half as from a free-kick. David Noble laid the ball to Michael McIndoe who hit it with a great left-footed strike, but it flew just wide of Myhill's right-hand post.
On the stroke of half-time Bristol were reduced to ten men as McAllister received his second yellow card after he took down Sam Ricketts with a late challenge on the left-hand side of the visitors' box.
Dean Windass created a chance for himself early in the second half, but the frontman's turn and half-volley from inside the area was easily saved by keeper Adriano Basso.
Hull fans felt they should have had a penalty late on in the game, as it looked as if Bristol keeper Basso had brought down Richard Garcia with a late challenge in the box, but the referee immediately turned down the appeals and waved play on.