I think think your body will tell you if you should be running or not, and I don't think you will cause more damage by running. My story and experieces below.
I had this same injury last year, except mine was a little bit worse. I had pretty bad pain, and numbness down my left leg extending all the way down to the top of my foot. My injury was at the same level as yours, and my disk was "ruptured" with multiple fragments.
I woke up one morning to find that I couldn't do something as simple as putting on my shorts secondary to the pain. My back had hurt pretty bad for about 3 weeks before this, and although I don't know this, I think that I probably had a herniation for quite some time. My back has hurt since I was 16 and running on the Track and CC teams at school, and I guess with my size, I am prone to these sorts of problems. I am tall, but not overweight.
The big difference in our injuries, though, is probably the extent of pain, numbness, and tingling I was having down my leg. Because of the dysfunction and on the advice of my neurosurgeon and several personal MD friends, I decided to have the surgery as I felt I really didn't have any other choice. My job requires some heavy lifting of patients, and I didn't want to let this thing linger and be off work hurt all the time. I also have young children, and I am very active in the outdoors and with playing sports, so I wanted to get "fixed."
I had an L4/L5 discectomy the end of June last year. Recovery is no fun, but with therapy and time, I can do everything I could do pre surgery. I still have pain, but really, it's nothing more that I have been used to, and I just tolerate it without narcotics to kill the pain. I take Celebrex 200 bid which imo is a wonder drug, not only for me, but for many of the patients I have as well.
Before I had this happen to me, I would have told anyone to not have back surgery until the pain or disfunction interferes with your activities of daily living and/or wakes you up at night, and I still tell people that.
I have played competitive basketball, and I have run since my injury. The running does not bother me at all. I also play golf as frequently as I can. Someone above mentioned good thorough stretching, and I will agree that is very important. Back exercises are also useful.
I too was only 29 when this happened, so it's not the end of the world if u do have to have surgery. I would recommend that you do follow up with the neurosurgeon like planned and see what he has to say. I also think you are wise seeing a neurosurgeon as opposed to an orthopedic surgeon. If the injury is not painful, and you do not have effect in your legs though, I would consider not having the surgery until that point. Good luck!