I haven't dealt much with Bradford's before, but I will agree with Todd in saying that they typically don't have huge problems with surface roots, at least that I'm aware.
Trees with evident surface roots of substantial size have typically run into some sort of physical barrier which restricts their journey in a somewhat downward direction. Now don't get me wrong, I don't mean that all roots grow straight down like that of taproots, I just saying withing the top 12-15" of soil. Examples of an impermiable barrier could be a heavily compacted layer of clay that had black top-soil placed over top of it. This is highly likely in todays unplanned urban environments. All thought and money goes into the actual building and visible vegetation, and not enough R & D into soil structure and horizons. There could be other reasons too, but this is a good place to start.
If you could get your hands on a soil probe to take a sample, you could easily find out if this is your problem or if you are dealing with something else.
If your patio is going to be built directly over the root zone of the tree, I would also give serious thought to removing the tree. Todds explanation of the majority of roots in the top 12" is right and if you have to dig down, then compact to achieve a solid base, you will most likely end up with a dead tree. Also, if there is an impermeable barrier a few inches down, the digging may remove all of the trees roots!