I've only used National Express (which is the only coach operator to serve Mildenhall) on a small number of occasions but I've normally found travelling with them a fairly relaxing experience. The only time that things were a little 'lively' was when we were 'entertained' by a drunken Irishman who claimed that he was Barry McGuigan's brother and was willing to fight anyone who would take him on. None of us believed his 'claim to fame' (and nobody was really too bothered about the guy anyway) but the next time I saw Barry McGuigan fight on the telly, there was a very familiar guy in his corner! ;-)
Depending upon exactly where you're starting from (and possibly the time of day when you'll be travelling) you'll have to travel via either Cambridge or Norwich, perhaps with one or more changes prior to that. Hanging around waiting for the next coach can be 'a bit of a bind' especially if you're left at an interchange point with very limited (or non-existent) refreshment facilities. (Drummer Street bus station in Cambridge is extremely basic but the new Norwich bus station is a bit better).
It might be worth looking into getting cheap 'Advance' rail tickets to Newmarket or Bury St Edmunds, and then taking local bus services from there.
BTW: I live in Suffolk and I sincerely hope that you don't think that Mildenhall (which, in my opinion, 'is a bit of a dump', is representative of out beautiful county!)
Chris