HELP! Need advice for Bike Wall mount
Drywall is not meant to support weight.

If you want to "do it right", fix the damage to the drywall by replacing a large section extending from one stud to the next.  While the wall is open, you can install a horizontal 2×4 between the studs (known as "blocking").  When you're finished, screw the upper screw of your bicycle mount into this wood, and it will support the weight.
The lower screw can go into a drywall anchor to prevent twisting, but not supporting weight.

A much quicker, but uglier, fix is to simply attach a horizontal 2×4 to the surface of the wall, properly attaching it to two studs.  Then screw your mount into that wood.  In your case, it would work best with two horizontals to properly space the lower screw.

I used this latter approach to attach a large wall-mounted TV whose mount didn't line up with the wall studs.

And the idea can be extended to surface-mounting a long horizontal 2×4 along most of the length of the garage wall.  It makes a convenient and secure place to install hooks, etc. for hanging equipment, hoses, tools, etc.