Can a person "catch a bladder infection" from another person? Person has had a urine culture test positive with e coli. Has been on antibiotics and has had a second test show negative.

No. This is not passed like a sexually transmitted disease, or from saliva or other contact. Germs get into the pee hole from the outside and climb into the bladder resulting in infection. It is a localized event & the germs come from nearby, often from the anus (stool) where it is a dominant germ.
E. . E. Coli is a bacteria found among the normal, healthy bacteria in stool and is the most common cause of urinary tract infections. Often, the infection happens from stool and bacteria entering the urethra and infecting the bladder by way of wiping improperly after a bowel movement, sexual activity, or just bad luck. This is more common in women because of the proximity of all the structures in that area. You cannot catch this type of urinary tract infection from another person. Some urinary tract infections are caused by sexually transmitted diseases such as gonorrhea and chlamydia. These can be transmitted through sexual contact with the infected person, but this does not seem to be the case with the person you mentioned.