regard vs bear on

regard is a noun but bear on is not a noun.

Word	Noun	Adjective	Verb	Adverb
regard	Yes	No	Yes	No
bear on	No	No	Yes	No

As verbs, bear on is a hypernym of regard; that is, bear on is a word with a broader meaning than regard:

Other hypernyms of regard include come to, concern, have to do with, pertain, refer, relate, touch, touch on.

regard (noun)	bear on (noun)
a long fixed look
(usually preceded by `in') a detail or point
paying particular notice (as to children or helpless people)
an attitude of admiration or esteem
(usually plural) a polite expression of desire for someone's welfare
a feeling of friendship and esteem
the condition of being honored (esteemed or respected or well regarded)

regard (verb)	bear on (verb)
deem to be	have an effect upon
look at attentively	press, drive, or impel (someone) to action or completion of an action
connect closely and often incriminatingly	be relevant to
	keep or maintain in unaltered condition; cause to remain or last