The most toxic emissions are probably NOx species. The catalytic converter takes care of most of these, but some do slip past. There are a few carbon based compounds that are pretty toxic too, notably benzopyrenes, and they are formed by any sort of combustion, even your gas stove at home. I don't know anything about respirators though, so I don't know what is good to keep these out.
I would say overall that your exposure to emissions doesn't change very much by biking instead of driving. Cars have air filters, but those are really only effective at removing particulate matter, any gaseous stuff will make it through. Wearing a decent respirator is going to make it a lot more difficult to bike too. Those things aren't made for use during exercise.