Is there a safe cycle route between Manchester and Salford?

Hi. I'm visiting Manchester for an event next week and need to get to Salford Uni. My train gets into Piccadilly station and It looks as if it's only a couple of miles from there to the Uni. I was hoping to cycle and Google suggests A34 (Princess/Bridge St) and then the A6 (Chapel St). Anyone familiar with this route?

If it's not a good route, can anyone suggest a quieter way? Thanks!