Can you invite guests to bridal shower if they are not invited to the wedding due to venue constraints?

You can, of course, but a great deal of tact will be required since it's only human nature for those not invited to the wedding to wonder how you reached the decision to invite others and not them.

On the other hand, there could be resentment if you invite friends to neither the shower nor the wedding!

One idea might be to make it a special shower, maybe with champagne and good finger food, and explain privately to each person not invited to the wedding how bad you feel at not being able to fit everybody in, but there simply isn't room.

Perhaps you could give them, privately again, a small gift - a keepsake - of the wedding and suggest that once you're settled following the honeymoon, you'll give a simple, intimate party just for them. Do this before the wedding, otherwise it might appear to some that you feel they're upset and are simply trying to pacify them.