Experiments suggest that the abberation you allude to is resolved by electromagnetic forces in the system. Evidence suggests that the speed at which gravity propogates is between 80% and 120% of c. Indeed experimentations suggest the number is equal to c within 1%. Link below.
Is gravity itself a fictitious force?
A few lines up, I wrote that the force we feel when the bus is braking, is weird in that its strength is proportional to our own mass. But what about gravity? That also has a strength that is proportional to our mass! Could gravity be a fictitious force too?
Yes, that's exactly how gravity is viewed these days. This is the content of Einstein's General theory of Relativity. Einstein conjectured that perhaps we've been looking at things in the wrong way. Newton viewed the orbit of a satellite, or the parabolic flight of a projectile, or the fall of an apple, to be complicated motions caused by the action of this mysterious force called gravity. But Einstein turned the problem on its head, and decided that satellites, projectiles, and apples are all following a motion that is as simple as any motion can be, provided they are viewed on the stage of a curved spacetime.