Bums is an onomatopoetic word for the sound of a collision, somewhat equivalent to the English crash or boom. It’s commonly used in children’s speak and was in fact one of the very first words my son could say. If boom or crash is used in an English children’s comic, it is likely to be translated as bums without anybody thinking about complaining. Going by this ngram, it’s probably older than bumsen or Dingsbums.
From this, you get bumsen, whose primary use is to describe a noisy collision or the sound made by it. I would strongly guess that the secondary use for sexual intercourse originated from the primary use (as a noisy collision of two people).
Dingsbums finally is a fusion of Dings (thingy) and bums. Here, I would guess that the choice of bums has no deeper meaning and was just made for the sound of the final product. Whatever, its origin may be, it’s lost nowadays and thus Dingsbums is as meaningful as the English doohickey or thingamob (unless I missed some special meaning of the latter two).
To conclude, the word Dingsbums has as much sexual connotation as the word fingernail or fishbone. Either way, it’s rather colloquial but (in my experience) not much more than other words with that function and it is not much less or better accepted than Dingsda or just Dings.
Was ist der Unterschied zwischen einem Plastiksackerl und einer Blondine? Das eine ist ein Dingsbums, das andere ein Bumsdings.I wouldn't consider it rude, but not part of the high language, which also reflects in this joke and pun on words.