If you're going to give it its own lane anyway you might as well make a proper tram (which will have higher capacity and a smoother ride for passengers).
Here's a picture from Naples, but they are common across Europe: http://cdn.c.photoshelter.com/img-get2/I0000bgbDBRzeRa8/fit=...
Buenos Aires used to have a tram, actually. In the nineties you could still see the rails, on the road as you describe. But buses replaced them in forties because as the city grew the ability to change where public transport could go proved to be very valuable.