Is it completely normal for a bike mounted on top of your car to wobble about at higher speeds?
I don't know if I'm doing something wrong in it's setup or if it's just the way it is.
i have it set up almost all the way over to the passenger side.

 

There are lots of factors and variables - how fast where you going (anything above 130kmh is going to wobble), weather conditions, side wind, how did you attach the bike but from eyeballing your pictures;

Looks like a thule bikerack
Looks like an outride or similar (quick release mount, front wheel removed)

Comparing to my setup Looks like you have it mounted 'backwards"
Best ive found is: Have the front wheel quick release (QR) mount to the front of the car, the less stable rear wheel nylon snap fix is best to the rear.
*you can swap/reverse the QR so the hand clamp is outboard - makes life easier

Also - If i were troubleshooting - id also review the rough torgue settings on both the QR for the front, and the nylon snap for the rear wheel.u have thru. They should be tight.
If your bike has thru axles and the additional adaptors - added complexity for you to root-cause.
Outside of that - check x2 rack mount points (BOTH rack to the cross bars/ cross bards to fixed roof rails). They are compatible/arent muppetted together.
finally:
*Your bike isnt a wacky fat tyre compo with tyres spilling off the trays? Are you seven foot tall with a bike frame the size of a sailing boat?

 

This is probably a better picture of it. It's the touring bike carrier from Mini.
I'm guessing there's just nothing I can really do. It only really wobbles after about 110-115 kph.

 

Aha - a front-wheels-on rack.
Not used the mini-branded touring ones but have put my bike on a mates other-branded model. The more upright front (vs a the systems you have a lower front of the bike as you remove the wheel) is a little less stable. No idea on the recommended safe limit for speed but id say you are close.

 

Setups like that, always make me think of this (especially, at the end of a long day of driving).

 

That's always one of my biggest fears. Forgetting and then going through a low drivethru or something.
luckily, with the full glass roof I'm usually very aware of it being up there.