Can l5 s1 bulge with nerve impingement cause the bladder to not empty properly?

Not really: The bladder emptying is controlled by the lower sacral nerves.

Pinched nerve: A single level disc bulge would not likely affect the bladder - I would look for other reasons.

L5-S1 bulge: No. S2, (racepinephrine)3,4 keep poop and pee up off the floor.....how we learned it in medical school. It is the lower sacral nerves that affect ability to void. Well below the L5-S1 disc, which would affect the S1 nerve root into the legs/feet. At 40 y/o could be dealing with some prostate enlargement which would cause some issues with emptying bladder. Best to be evaluated. Hope this helps. Good Luck.

No.: Spinal nerves have myotomes, which innervate certain muscles, & dermatomes, which innervate certain areas of skin. The L5/S1 myatomes wiggle the toes/point the foot. The bladder is in the S4 myatome, which also controls the anus.