Karen---I posted this on your other thread after finding the flights you mentioned on the BA website. I assume you booked this as one ticket, in which case it is a legal connection, and you are protected if you miss that second flight. There is a reasonable chance you will make that flight if your flight from Dallas is on time, and the line for non-EU passengers at immigration is not long. But those are big "ifs". If you don't make it, BA should put you on the next flight to Venice.
We did that same transfer when we went to Venice the first time, in 2003. I think we had about 3 1/2 hours, and made it easily, using the bus. But we were flying Business Class, so first off the plane, with Fast Track through immigration.
You can speed things up by choosing seats as far forward in your cabin as you can get. And let the flight attendants know you need to make the airport transfer as fast as possible---ask if they can give you a Fast Track card ( Indon't know if they can).
And take a cab rather than wait for the next bus---there should be a cab stand right outside T3 where you will land.
If your plane from Dallas is late landing, so late there is no chance of getting to Gatwick in time, stop at the BA help desk before you go to immigration---I assume there is one somewhere in T3. Ask them what to do---they should be able to change your boarding pass to the next flight. Then you can slow down and lose the stress.