There is a marina on the extreme SSW end of the bay. I've never seen boats coming or going from there leave the channel to explore the bay, they tend to just go straight into Tampa Bay.
When entering, be sure to start your approach to the channel from the white marker light. The channel is plenty deep, but it gets skinny at the entrance. Once you make the last turn into the bay it's wide open. I run the channel on plane all the time if there are no other boats in/near the it. I WOULD NOT recommend this for your first time in though.
Like tcijoe said, leave your anchor light on. If you're concerned, leave some other lights on, but it's not necessary. I would be shocked if you saw another boat above 15' in there. (unless it's me!)
A good alternative if you won't be able to sleep is to anchor just inside the Manatee River. I anchor here about 80% of the time.