Capitalization of bpm/BPM meaning beats per minute

This is really a question of style. Abbreviations (or, in this case, initialisms) are not necessarily capitalised, especially when all of the words would be spelled out without a capital letter: there's an example in the question where "beats per minute" is spelled out with minuscule letters.

Most initialisms either have a proper noun as at least one of the words, which may cause the whole to be capitalised, or the term is important in the document (eg Wikipedia's example of congestive heart failure [CHF]). It's very unlikely that a term like "beats per minute" needs to be made prominent in a sentence within a text. Setting it in capitals could upset the balance of the typesetting, and lowercase is easier than using small caps _^BPM.

If it might get lost, for example when filling in a form, it might well be capitalised.

   Heart rate: ________ BPM

There is an additional set of initialisms — acronyms, which can be pronounced as words — and where these are common nouns they are customarily set in lower-case: scuba, laser, radar, sonar and the like.

In general, units should not be considered as abbreviations, but symbols (see, for example, the SI brochure). So, for instance, the capital letter A is not the abbreviation of the unit ampere (ampere, with a lowercase initial, is the unit; Ampère, with a capital initial, is the scientist), but rather its symbol; similarly, J is the symbol of the unit joule, not its abbreviation.

That said, it should be noted that bpm is not a recognized unit in the SI (an acceptable unit would be min^-1), but treating it as any other unit can do no harm.