Bug spray is a touchy subject. Most experts recommend that you use a DEET based bug spray (with a max concentration of 30 percent) but you should only use it on babies over two months of age. I'm skeptical. DEET is a pesticide and is also not all that safe. You can talk to your baby's pediatrician about it; but note that I wouldn't use it on my own son, not when he was a baby, and not now when he's seven.
On the other hand, bug bites are no fun either. There are some other options besides DEET based sprays for your family.
Buzz Away outdoor products: DEET free and has won many awards, including being rated the number one Natural Insect Repellent In Independent Tests by the Good Housekeeping Institute Report, The National Parenting Center and the University of Guelph. Deet-free insect repellents from Consumer Reports - a great read.
World Travel Guide has some bug based natural anti-itch products reviews - three products are featured and two are kid safe.
If you decide to go with a DEET based product read this article from the American Academy of Pediatrics Committee on Environmental Health: Safety Precautions When Using DEET on Children. Also from the American Academy of Pediatrics: DEET Alternatives Considered to be Effective Mosquito Repellents