3yrs plus biting

I have a 3 year old daughter who doesn't have any issues with language (in fact quite articulate) she has excellent recall, but has been continually biting  for more than 6 months.
I have tried to consistently enforce the following: remove her from play, as well as confiscating toys, rewarding non-biting interactions  and getting her to apologise.
I have tried talking to her about why she has bitten and her usual response is "because I was having bad behaviour "(a term used by us). She is able to describe other interactions in detail eg "I was putting on my shoes because I want to go outside" but can't say why she has bitten some-one.
She has bitten her dad and myself on many occassions (usually when she is being put in time out for other misbehaviour or is over excited and having fun). She has also bitten her grandparents and very frequently bites her younger cousin (2 1/2 yrs) seemingly unprovoked.
I have tried to look for patterns of behaviour that preceed the biting (eg hunger, overtired, over-excited, frustrated) and eliminate these but biting still persists. The only factor I can pin-point is that she generally only bites adults and children she knows really well.
I would appreciate any advice you can give