Sorry, but bis is good Latin for 'twice'; cognate with Greek dis, Sanskrit dvis from PIE *dwis.

You are quite right - for some reason I thought that the Latin "bis" was borrowed directly from Greek.

On the subject of "-ter", we also have
ob -> obiter
prope -> propter
post -> poster(us), poster(itas)

But in the cases of intra, contra and ultra, I think we may be seeing something different; contra especially is quite semantically different to cum/con, more than can easily be explained by a comparative ending. Originally I was looking for a noun like "*tera", but there is a stem "tri" in Sanskrit meaning "to step over/go beyond", which is surely related to L."trans" and could be the missing semantic ingredient in these words.