both Shawn and Joanne are right in pointing out that you need to work as part of a team with the doctor and/or PT. However, having a bulging disc by itself does not have to throw you into confusion.
If the situation is a recent problem, working with the PT is mandatory. But you will find a lot of people with bulging discs who are asymptomatic and go through the day without pain. In that case, you may even get a physician’s approval without any restrictions on exercise. Ask whether they ever saw a PT and ask for a list of the exercises that they got.
In any case, I do my own assessment as with everbody else. If I have PT exercises, I start with those and watch how the client is doing. Else, I start very conservatively (lying down, pelvic tilts, teaching neutral spine), observing the client like a hawk to see whether my posture cues can be translated into correct movement. I saw that you train at a gym, and that may tempt you to put a client on machines. Be aware that correct posture there just as important; people often get a false sense of security with machines.
However, there may be more to the client than what I am describing. If you feel that your skills at this point in your life as a trainer are not up to the task, you will do yourself no harm in saying so.