Venting my grow tent

So I moved my grow tent into the bathroom so I could vent through the bathroom fan. I removed the front grill and light housing along with the motor. One issue I ran into was that I could not remove the whole exhaust box. I couldn't find an screws or any sort of method of attachment. The box does wiggle around like it is loose but just one side does not seem to want to budge. I can free the ducting running the box. feels like it might be being bent at a pretty hard angle. So I took the plate the motor was attached to and taped the ducting from the tent through the hole. and put the plate back in hope the air would find its way through the duct. This is an older apartment from the 80s and I have no access to about the roof. I figured the exhaust box was attached to a stud above the ceiling. The issue I am running into now my rigged duct tape comes partially down every day. I am guessing it is due to the pressure because the bathroom vent isn't taking the air properly? Any insight would be nice.

I have a hard time picturing it based on your description, how about adding some pictures? But high quality duct tape vs low quality can make a huge difference. The cheap stuff will go loose because of moist usually. A flange with clamp usually works best.

Sorry for not including the picture and sorry for the picture being a little dark. Since the ducting is going into the part where the light was in the fan the bathroom is a little dark. But I am using duck tape brand duct tape, any advice on a better type? And what type of flange would I get that could fit this task.

Get some insulation and wedge it between the ceiling and ducting on all sides til its pretty tight. Maybe balled up newspaper so its just not hanging.

if the vented air is hot, it will reactivate the glue on the duct tape and it will fall off. use high quality hvac tape (foil 3m flexible type). i use the 3m hvac tape for any taping needs that will have direct hot air contact, and gorilla tape for all other taping needs. the hvac tape is made to so it doesnt unstick like reg duct tape.