The best feature that I haven't been able to find is someone to carry my bag for me. Ha Ha.
Anymore, competitive bowlers must bring with them more balls than they can safely carry at one time. Even 4 balls are difficult to drag around on your shoulders for any length of time. Therefore the wheeled bags have become very common. My biggest problem with these is the width of the 4-ball bags considering most bowling alleys do not have large enough concourse areas for two lanes of traffic with these big bags. I prefer the inline 3-ball bags for this reason.
Now that I've shown my preference for wheeled bags, I will list the most important features for them. The wheels must be large and very rugged with the ability to withstand a pounding. I haven't seen it yet, but I would like to see an arm stick out from the bottom of the bag that would set up high enough so that the weight of the bag is not supported by the wheels when the bag is horizontal. Anything to relieve pressure from the wheels as much as possible would lengthen their lives. I also look for a bag that is tall enough so that I don't have to bend over when dragging it behind me. The 3-ball bags work well for this, but most of the 2-ball bags don't have a long enough handle. For those that have difficulty lifting a 3-ball bag into their trunk a two ball bag with a long handle is great.
For any bag, I want a large area for shoe storage. My shoe size isn't huge, but I like to use shoe bags and several bowling ball bags don't have a big enough compartment for these. Another great feature is to have a padded area for the balls with a strap to secure them down. Again this goes back to the pounding they may take especially on the airlines. We've all got several dollars tied up in balls and they need protection. I also like the removable accessory bags that have popped up in recent years. These are great when you have access to a storage area for most of your equipment and only have to worry about a couple balls and your extras.