There are actually three words here. The simple one is the big growly creature (unless you prefer the Winnie-the-Pooh type). Hardly anyone past the age of ten gets that one wrong. The problem is the other two. Stevedores bear burdens on their backs and mothers bear children. Both mean “carry” (in the case of mothers, the meaning has been extended from carrying the child during pregnancy to actually giving birth). But strippers bare their bodies—sometimes bare-naked. The confusion between this latter verb and “bear” creates many unintentionally amusing sentences; so if you want to entertain your readers while convincing them that you are a dolt, by all means mix them up. “Bear with me,” the standard expression, is a request for forbearance or patience. “Bare with me” would be an invitation to undress. “Bare” has an adjectival form: “The pioneers stripped the forest bare.”
2) BASICLY / BASICALLY
There are “-ly” words and “-ally” words, and you basically just have to memorize which is which. But “basically” is very much overused and is often better avoided in favor of such expressions as “essentially,” “fundamentally,” or “at heart.”
A “bazaar” is a market where miscellaneous goods are sold. “Bizarre,” in contrast, is an adjective meaning “strange,” “weird.” Let all those As in “bazaar” remind you that this is a Persian word denoting traditional markets.
4) BEAUROCRACY / BUREAUCRACY
The French bureaucrats from whom we get this word worked at their bureaus (desks, spelled bureaux in French) in what came to be known as bureaucracies.
5) BECKON CALL / BECK AND CALL
This is a fine example of what linguists call “popular etymology.” People don’t understand the origins of a word or expression and make one up based on what seems logical to them. “Beck” is just an old shortened version of “beckon.” If you are at people’s beck and call it means they can summon you whenever they want: either by gesture (beck) or speech (call).