Ten is by far the most human-inclined incarnation of the Doctor in the NuWho era (I haven't watched the originals), and Bill's natural emotional intelligence and trust in humankind would in my opinion make them one of the best functioning Doctor-companion pairings in the show.

Edit: Just to make myself clear, I don't mean they'd work well as a narrative device, because Doctor-companion differences in opinions and beliefs are one of the most interesting plot resources of the show. I just mean they'd be really good friends (plus, no risk of the cringy, non-reciprocal romantic interest in the Doctor that somewhat killed the interest of Martha's character).