Think I know the answer already …
Just had my Cove serviced, including Hope Minis bled, etc. Everything was working perfectly till I had to shove the frame and wheels in the back of the car. Having put the wheels back on, the front one isn't spinning freely, and the rear lever pulls all the way to the bars.

What do I need to do to get the brakes back to normal, and how can I stop it happening every time I have to take the wheels off?

Yours, sheepishly!

make sure you don't pull the levers next time the wheels are off.

stick a flat headed screwdriver in between the pads/pistons and gently lever them back into the caliper.

the rear should sort itself out after a ride if you store it the right way up. if it doesn't go back to the shop.

The brake lever's got squeezed in the car. Push the pads apart again with a blunt tool (some plastic tyre levers are good. A screwdriver if you take care not to chip the pads). In future, put a plastic spacer between the pads. Your bike shop should be able to provide some free. Or use some thick card.

Sounds like you may have accidentally pushed the levers when the wheel isn't in. For the back brake just pump the lever a few times (with the wheel in) and it should some back to normal. For the front one, take the wheel out, prise the pads apart using a flat bladed screwdriver or similar, then put the wheel back in and pump the lever a few times.

it could be that they were bled and not pumped back to position?
pump the lever a few times and see what happens?
you may have pulled the front lever while the wheel was out and its moved forward?
they SHOULD realign themselves.

I do all my work myself personally, but in my opnion, your better off doing your brakes yourself for sure.
a LBS wont take as much time and care over it as you would, no fault by them, but if they have several bikes to do, and a time limit, you dont spend 20 mins chasing a single bubble.
a basic correct bleed and move onto the next one.

Instead of pushing the pads back – push the pistons back – just behind the pads. Lever the srewdriver behind one pad and lever towards teh pad so both pads make contact – this will push th opposite piston back – then reverse. That way you wont damage your pads!