Motorcycle pulls to the left?

I have a 2000 Honda Shadow 1100 Spirit. When I let go of the handlebars my bike pulls to the left. I just got two new tires mounted and balanced as well. Is this normal and should I worry? It is only when I let go (which I don't do often as I don't even have cruise control)

If it didn't do that before the new tires I would take it back to the tire store and ask them to re-mount the tires.

It may be how the wheel was mounted after the tire was installed. Go back.

Your rear wheel is misaligned.

Are you sitting exactly centered?

I forget whether the 2000 Shadow 1100 has shaft drive. If it's chain or belt drive, the tension of the chain or belt is adjusted by moving the rear wheel back and forth, and there are adjusters on both sides. The adjusters have to be adjusted together. If they aren't exactly the same length, the back wheel will be turned a tiny bit one way or the other, so when the bike is going straight it feels like it's turning slightly to the left or right. They ought to be able to check this for you wherever you had the tire put on.

Rear wheel alignment is one possible problem- a worn swingarm bushing either side can cause it with left side most likely. Front end alignment of lower and upper tree can also cause a 'drift' - you note it is when handler bars loosened, not a hard pull constant as might be from a bent front tube from possible crash. Rear bearing check, front end tree and fork alignment check needed - a long straight edge for front can be a good 2x4 furniture grade. As for the cruise control? You can make one with 2 hose clamps and a $1.49 hardware store 4 inch angle bracket. I use them on Goldwing and Suzi 650- simple, cheap and works by resting wrist on the upright end of bracket that has been adjusted to give about 4000 rpm cruise from straight wrist resting with loose grip. Slight drop of wrist and get 4500 rpm- so I can cruise at 60 to 75 with minimal effort and no tight grip.

It is possible for a mechanic to install the front axle improperly.
Bring the bike back to the shop.

Frankly, I don't think there's anything wrong with your bike. Bikes are hard to keep in a straight line with no hands on bars. Do you ride with your wallet in your back right pocket? This will put your weight to the left. And there's the road camber (if you are in the US). This will make a bike pull to the left. It is NOT rear wheel alignment (its a shaft drive).
Just ride and keep at least one hand on the bars.