Have had a similar problem, slab concrete replacement driveway ended up resting a couple of inches higher than the slab in the garage floor. What to do about water coming in and dealing with the height difference.
In your situation, since you have soil between the asphalt and garage as well as a decent amount of space, digging out a drain trench between the asphalt and the garage will let you put in a length of slotted french drain pipe to control water and use rock and pavers to smooth out the difference in heights of the two surfaces.
Dig the trench a couple of inches deeper than the pipe to allow you to wrap the pipe in weed blocking cloth (to keep it unclogged), then fill in the space around and above the pipe with whitewash rock. Fill in the rest of the area with the rock sloping the surface until you have about 1 1/2 " edge of asphalt and garage showing above the rock. Cover the rock with 12x12" landscape tiles (gray color if you want them to not be noticable, red ones if you want to make the spot more safely marked). You can then run your motorcycle over the area smoothly. If you happen to run a car tire over the area, the tiles are large enough to take momentary pressures since supported by the rock. I have put in a couple of hundred feed to french drain using this method and it works fine to control the water, makes a decent walkway and always looks nice.