The stabilizer bar is great if you want to jump in the dark or while watching TV and you don't want to have to focus on your stabilizer muscles in your legs to maintain balance. Even with a Cellerciser that has the most even bounce of all rebounders, I still use a bar. You cannot do strong frontkicks and side kicks to work the outer leg muscles if you don't have the bar. Otherwise it will throw you off the rebounder.
The Cellerciser and Needak have the most stable bounce of all the rebounders I have tested. The Lymphaciser company doesn't even make a bar with their rebounder because its not made for people to jump any higher than a few inches out of the mat. When doing the health bounce it is hard to lose balance but after about 20 minutes many people like to hold on to something, especially if their calves get sore from jumping. With the health bounce, as you land on your heals and then push of with your toes, beginners get sore calves and often like the bar to push of with their arms to take some of the weight off their calves.
Getting the bar with a spring rebounder even if you don't have balance problems, you can't do the more advanced exercises.
With a bungee rebounder, most of the people I talk to call back and get the bar. Jumping high on a bungee rebounder almost always loses balance as you land if not looking directly at the mat or if focused on the TV its easy to lose balance. The larger smaller sized Jumpsport really doesn't require a bar as much as the larger 44 inch models.
Getting a bar with a spring rebounder is usually necessary if you have balance problems.
With the bungees, you really can't do the lymphatic health bounce. So, if buying a rebounder for lymphatic cleansing is your reason for buying a rebounder, the bungee makes you jump very high out of the mat to get G force that you can't just bounce an inch over the mat and do the Health bounce. It's all about repetition more than G force but their has to be just enough G force to open the one way valves in the lymphatic system to drain lymph.
The bungee rebounders at at class I went to in NY had hexagonal rebounders. They all have bars for a reason. It is very hard to keep balance if on a larger bungee rebounder. With the bar rarely people get injured.
The balance bar for the rebounders just gives extra balance, especially for seniors that have low balance.
If children are going to be jumping its better to have a balance bar as they like to jump high and often fall off. If the bar is on there they usually naturally want to hold on to it.
The balance bars are easy to take on and off. The Cellerciser bar is a little harder to put on but it has the wobble feature so that the bar is not set in place. If you bounce a little forward or backward, the bar moves with you a little bit. Only the Cellerciser rebounder has this feature as one of their patents. So if you jump backward a little, the bar is not so set into place that it moves the rebounder back. The Cellerciser balance bar has the best feel of all the rebounder balance bars I have used. It also has height adjustments.
If you are going to be jumping high on any rebounder that has uneven bouncing I would always recommend the bar if doing higher bouncing. By this I mean it's a good idea to have a balance bar when the edge is much more firmer around the edge and very soft in the center. Some rebounders have a drastic change in yield of the mat while others its more gradual. The Cellerciser is the most gradual and Needak the second most gradual yield change. These are the only two rebounders I have found that you don't necessarily need the bar unless doing advanced exercises.