convenience, facility, excrement, feces, letter, chance
便 centers on making things easy and smooth: convenience, a useful facility, or a favorable chance. The letter sense is a natural extension of easy communication, while the excrement/feces sense is a euphemistic application of bodily convenience.
便 combines 亻 (person) with 更, which likely contributes both sound and the idea of changing or passing through, suggesting a person making things flow smoothly.
A person 亻 beside 更 (change) suggests someone adapting things for ease: making life convenient, sending a letter, or taking a chance. Even the bathroom sense fits—making a bodily process convenient.
For ベン, imagine a person using a convenient bench to rest while writing a letter: bench -> ベン, and the person 亻 finds it so easy.
flight (e.g. airline flight); trip (e.g. train trip); sailing (e.g. ferry voyage); service
convenient; handy; useful
mail service; postal service; mail; post
constipation
inconvenience; inexpediency; unhandiness
taking advantage of (an opportunity); jumping on the bandwagon
toilet; lavatory; water closet; restroom; bathroom
convenience
urine; piss; pee; urination
convenience; accommodation; advantage; benefit; expediency
TA-Q-BIN (express home delivery service provided by Yamato Transport)
news; tidings; information; correspondence; letter
gentle; peaceable; amicable; quiet
feces; faeces; excrement; stool
writing paper; stationery; notepaper
surface mail (by ship); sea mail
convenience; handiness; usefulness
express home delivery service
regular service
non-stop flight; direct flight
airmail; air mail
special delivery mail; express delivery post
post office