Is it possible to build a tanning bed/canopy myself using tanning
bulbs and a light fixture? Has anyone tried to do this successfully
and have some advice or plans?

I searched for homemade tanning bed and didn't get anything.

Yes you can, but check the electricity that it would give off because
it would use a lot of electricity and your bills would go through the
roof. You would also get someone to look at the circuits. So it is
possible, but your bills would take a chucnk out of your account so i
would advise agaisnt making one.