Can wearing a slightly lose bandana or a beanie hamper the growth of transplanted hair?

Wearing a hat or beanie one month after surgery should be fine. If you're concerned it's a good idea to check with your doctor.

You are 36 days post op you can wear anything type of head covering (hats, bandanna, beanies)  you would like and cause no harm to your transplanted hair. YOur exercise activites can resume to normal as well. 

At this time you can do whatever you want, wear what ever you want and do all of the exercise you want.