How much bacteria is there on shopping cart handles?

Not enough to worry about unless you have a medical condition or illness which plays havoc with your immune system.

The proliferation of antibacterial soaps, wipes, sprays, cleansers and the like is actually causing more problems than anything else. That's because the bacteria then becomes resistant to these antibacterial agents, causing the need for stronger and stronger products ~ and breeding stronger and stronger bacteria.

Stop using antibacterial products if at all possible. Instead, focus on basic hygiene (hand washing with soap and warm water, using a tissue when you cough or sneeze, etcetera) and a healthy lifestyle. That will go a long way towards keeping you relatively 'bacteria free.'

P.S. Studies have shown that children who are exposed to normal amounts of dirt (read: bacteria) are actually healthier than children who live in germaphobic clean freak households. As my grandfather used to say, "You've got to eat a peck of dirt before you die!" 

It is a case-by-case matter.  If one of the store employees just used that cart to tote trash to the dumpster, or collected up all the drippy, expired packs of raw chicken, there could be a lot of filth on it.  Or if the last customer to use it had a raging cold or some other virus, they probably left some "bugs" on the handle.