It sounds like your bi-fold doors and/or track are not properly installed or adjusted. While lighter weight ones are flimsier than heavier, all wood, ones, they all should work better than you describe.
Make sure the track and hinge pivot mounts are securely installed. Then, make sure the doors are square to the track in both the open and closed position. The bottom hinge pivot plate is adjustable for this.
Raise the height of the door via the threaded lower hinge pin. There should be just enough clearance between the door and track to allow smooth operation.

Alternative doors may be bi-fold doors that have no track. The ones I saw were a custom installation with magnetic catches to hold them in both the open and closed position.

An accordian door might also work, but they extend several inches from the doorframe in the open position.