Usually--if you still get a frost at night--that will kill new crabgrass seedlings.
Since its is likely both products contain fertilizer, you don't want to use both fertilizer treatments in the same week. The Bermuda cannot actually use the fert until it starts to green up. But you probably cannot find a crabgrass preventer that does not have fertilizer in it, also.
Best would be to apply a liquid weed control--like Ortho Weed B -Gone. If you want to use a weed and feed product, you should wait about 5 weeks after the first fert treatment to avoid excess and reduce contamination of ground water.