Design an experiment to determine the source of the pathogen?

Isolate the bacteria from the honey and identify them.

You should never give honey to a baby.

You are looking to fulfill Koch's Postulates.  You will need to make sure the Pathogen is present in every case.  Then Isolate it from the Host.  After Isolation, you will need to infect a new, susceptible host.  Finally you will need to re-isolate the pathogen.  I would look up Koch's Postulates if I were you.  

Good luck

Typically in a food-borne disease outbreak investigation you would first do a stool culture. Then, you would try to isolate the organism from the food. You would then get the subtype(s) from Pulse-field gel electrophoresis (PFGE). If the subtypes match, you can be pretty sure that the source of the pathogen is the honey.  

The only tricky part here is that you mentioned honey, and infant. Which makes one think of Botulism. Botulism is caused by Clostridium botulinum, which is an anaerobic spore forming organism. The bacteria are not present in the honey, but the endospores are. So, in order to isolate the endospores from the honey, and allow the pathogen to grow, you would need to follow strict procedures. The 1979 JCM article referenced below describes one method, although there are probably polymerase chain reaction (PCR) methods available today.