When you're running a bungee cord from one side of the tube to the other, at the top, you're place a bit of stress on the bladder, but not enough to create possible bladders failure. However, you are causing the surface abrasion on your bladders cover as the cord rubs back and forth. This will reduce your tube's material lifespan at the contact point. If you're planning to run it below, same thing. Another thing about having a bungee cord holding down the rack is you're forcing two sides of the tube to come together under the tension of the cord. That decreases the effectiveness of the tube gliding through water, such as directional control and stability. This is why modding your tube for racks on both sides, we utilize a crossbar behind the seat. This stabilizes the racks during movements, as well as create an additional holding capacity for your rack overall weights.
For a Cumberland, there are plenty of space in the back of the seat for housing the net there, to get the net out of the way, preserving that empty spot for the spare rod, or just an empty location for rod holding during trolling. A large net sticking out on one side will create too much instability, unless the net is one of those small short handle trout net. In either case, toss the net in the back of you, or mount the net running horizontally with your bladder on either side.