Yes.

Although you better hope your Bartlett doesn't pollinate the Bradford because then it could cause a bunch of mutant baby hybrids to spread with a vengeance. Birds will eat the little fruits that form on the Bradford and spread the invasive seeds out into nature.

Your Bartlett pear will contain these evil hybrid seeds too, but normally birds are not able to carry away the big pears.

From what I've seen Bradfords bloom before any of the euro or asian pears I have so I wouldn't worry about it.

Ornamental, Euro and Asian pears can cross pollinate. You just need them to bloom at the same time to make it work.