"Red tape" is a pretty common idiom here. It's similar to bureaucracy, but it's more like the useless stuff you have to deal with in order to do something.

Say you want to update your driver's license and you need to bring in some ID and fill out a form. That's regular bureaucracy.

If you want to feed the homeless so you have to get a permit for an event, prove your volunteers have food-handling training, fill out forms for your volunteers, notify the police that there will be a public gathering, schedule an inspection of the facility, etc, that's red tape.

Another way to look at it might be that Bureaucracy describes the system in which offices communicate with each other, and Red Tape are the tasks/forms/whatever you have to complete in order to get what you want approved.