Bedding occurs around the full moon of every warm month. Once the water temp hits around 67, you can start looking for spawning bream. Here in Georgia, the spawn usually starts in May and continues until August or September. Shellcrackers spawn a little earlier in the year.
I usually don't focus on spawning bream, though. The fish are still there the rest of the year and are pretty much ignored by other fishermen at those times.