Attach piece of wood to wall, with need to be removed often
French Cleats

Could you use a french cleat? They are commonly used for demountable fixing of items to walls, including quite heavy items.

If necessary, they can be recessed so that they are entirely invisible



They are easily made from wood but you can also purchase aluminium or other metal sections designed for this purpose.

Threaded inserts

You can put a threaded insert into a wooden stud (or into a wall cleat as above). This allows you to use a machine screw (bolt) instead of a wood screw.
A machine screw into a metal insert will stand up to repeated removal and replacement better than a wood screw.

Just one (or two) of these could be inserted into a wall cleat and used to lock the other cleat into position.

Alternatively, if you have wooden studs in convenient positions you could use these directly in the stud. It might be a little fiddly to align everything when reattaching your item to the wall.



Some inserts are hammered in, some screwed in using a hex drive (allen key).
You need to drill the correct sized hole to receive the insert.