As far as I can tell, kompati doesn't have the additional degrading (and/or mocking) meaning that (to) pity often has.
ReVo lists the following translations to English:
- have compassion for
- feel compassion for
- have pity for
- have mercy on
- be sorry for, commiserate with
One can easily recognize that compassion and kompati have the same root (ethymologically, not regarding Esperanto's radikoj concept for word stems) and I feel like the respective translations capture the meaning of kompati much better than those with pity. I'd say the most generic translation of kompati <personon> is (to) feel sorry <for someone>, but mostly without the paternal looking-down-on nuance that also feel sorry can sometimes carry.
What should B. say?
What would they say in English?
While kompati might not be as degrading as (to) pity, "Mi kompatas vin." still to me doesn't feel like something one would reply to someone expressing sadness in everyday conversation, just like one doesn't usually say "I feel sorry for you." unless the person suffered a severe loss, such as death of a loved one. Saying it directly to the sad person in less severe situations feels a bit too declamatory/solemn (German "pathetisch", which isn't quite the same as English "pathetic") to me.
Saying it about someone to someone else is quite natural, though: "Mi kompatas ŝin." — "I feel sorry for her." / "I feel with her."
I don't think that "mi bedauxras" would work, because "bedauxri" means "to regret", right?
bedaŭri (PIV, ReVo) in fact has a wider meaning and can be (and often is) used for things that aren't the subject's fault. "Mi bedaŭras." or "Mi bedaŭras tion." can be used for both, apologizing and to express compassion (also for malice not caused by the subject) in a more casual way than "kompati". It probably comes from the German verb "bedauern".
There seems to be in fact a (AFAIK less common) verb to express only regret: penti (PIV, ReVo)