I have an olde english bulldogge who does the exact same thing. I also have a chiweenie who loves squeeker toys and my bulldog loves to chew toys like bubble gum until the squeekers break lol. I have certain toys I try to keep only for teh lil dog but my bulldog always winds up gettinga hold of them.
Unless its a heavy duty rubber toy my dog will destroy squeekers and stuffed toys literlaly in a matter of minutes.
Here is one toy thats great for bigger rougher dogs, its a tug rope, you don't have to use it to tug as I know some people dont like teaching their dogs tug of war, especially pitbulls, personally I like playing with my dog like this he knows when its play time and when not to fight iwth me for things. I like that its a long rope too as shorter ropes my dog tries to work his way up the rope nad eventually winds up at my fingers lol but this is long enough to have plenty of room to play with and still keep some distance. Also if you prefer shorter ropes you can cut this into 3 or 4 shorter lengths and it saves money over buying shorter ones anyway. I believe its a 72" Dog Rope Tug Toy and only $16 and some change on amazon. I'd pay almost hte same for like a 1 or 2 foot rope at petsmart or walmart or whever.
THey are fun if you have two dogs as well. I get my bulldog and my chihuaha playing tug of war and entertaining each other playing with it as well.