I want to argue that the lack of inflection for sg. der Busen, pl. die Busen, and what looks like an inherent plural ending points to a plural stem, or potentially dual.
Dual number was alread lost in the common language stage whence also bosom, but there is for example Tür(e), like door, from Proto-Germanic (PGem) *durz: "Likely back-formed from *dʰur-ih₁, an old neuter dual form, ..."; "This word was a plurale tantum in Old Norse, and it might have been used in that way in Proto-Germanic as well. ...". (en.wiktionary; cp. Kroonen, EDPG, 2013)
reflexion requires that the ending has left traces validating the hypothesis. The singular to Busen should be *Bus-, *Buse, theoretically speaking (cp. ''Hose, -n''; NB: ''pantalones, trouser, pants'' are pluralia tantum, and I like to joke that "mein Hosen" sounds natural, too). The schwa'ish -e might be a phonologically erroded reflection of the ending.
Wolfgang Pfeifer notes: "ahd. buosum (8. Jh.), mhd. buosem, buosen ‘Brust, Schoß’, frühnhd. busam, bosam, asächs. bōsom, mnd. bōsem(e), mnl. boesem, bōsem, nl. boezem, afries. bōsem, aengl. bōsm, engl. bosom führen auf westgerm. *bōsma-. Herkunft ungewiß. ..." (cf. DWDS.de). This is in agreement with PGem. *bōsmaz: "Exact origin unclear. Possibly from Proto-Indo-European *bʰōw- (“to inflate, swell”); or from earlier *bōhsmaz ("the space between the arms"; compare *faþmaz), from Proto-Indo-European *bʰāǵʰus (“arm”), whence *bōguz (“upper arm, shoulder”)." (en.wiktionary)
I haven't thought this through when setting out to write this up. The derivations from *bōguz are wild. To stick to the plan and to stay on-topic the discussion of the further etymology should be kept to a bare minimum, accepting uncertainty as a premisse.
The High German -n is a regular change.
Old Saxon (cf. wiki) and Middle High German reflect an ending, sometimes. Otherwise, lacking an etymology, the ending *-a(z) is not waranted, and might have become leveled.
The evidence is chiefly West-Germanic, but the language reality of a Proto-West-Germanic branch is debatable. We do see early Latin loans at this stage. There are compatible etyma for mamma "breast", and Greek μαστός m. (mastós, "breast"). Sinus ~ Meerbusen seems to be a much later calque from Latin (cf. DWDS; post-hoc ergo propter hoc).
Naturally, there exists a wide variety of synonyms and more so euohemism. Nevertheless familiar terms are supposed to conservative and stable as a heuristik. ''Busen'' appears rather clean to me.
The meaning has been questioned before: Is "Busen" just the area between the breasts?.
Question: Do you know a striking hint either way for or against the assumption that Busen reflects a dual number?
PS: I'll also mention beide, cf. PGem *bai ("both", f. *bōz, n. *bō),