Like many words in the English language, bear and bare have multiple meanings and can function as more than one part of speech. For the sake of brevity, we’ll only be covering the most commonly used and confused meanings of the verb forms.
For bear (used with an object), dictionary.com lists over 30 definitions, which include the following:
1. to suffer; endure; undergo.
2. to sustain without yielding or suffering injury; tolerate (usually negative).
3. to hold up under; be capable of.
These definitions, which fit the meaning in Anon’s question, convey the idea of withstanding something, which is generally negative.
To have Lily hating him hurt more than Severus had imagined; even so, the sting of her pity had been much harder to bear.
"Your mum can’t be reasonable about this, Ron," Hermione said gently. "She went through it before. It’s no wonder she can’t bear the thought that more of her family might be killed, now You-Know-Who is back."
Other common meanings are
4. to hold up; support: to bear the weight of the roof.
5. to hold or remain firm under (a load).
6. to carry; bring.
These suggest the idea of carrying a physical load of some sort.
Without magical assistance, there was no way the bottom-most walls of the Burrow could bear the weight of the many floors piled on top of them.
Hagrid lifted the unconscious Buckbeak onto his shoulders to bear him away to the Magical Creatures Clinic.
The final most commonly used meanings of bear are
7. to bring forth (young); give birth to.
8. to produce by natural growth, as in a tree that bears fruit.
These have to do with the idea of producing offspring.
No sooner was Fleur married to Bill than the bets were on to see how soon she would bear the first Weasley grandchild.
The verb bare (also used with an object) means
1. To make bare (as in without covering); uncover or reveal.
2. To expose."Who’s so short he has to stand on a box to kick a duck in the butt?" Ed hollered. He bared his teeth and launched himself at Russell, arms flailing wildly.
Alex Louis Armstrong ripped open his shirt to bare his chest, the better to show off his muscles as he expounded on the fine alchemical techniques passed down in his family over the last several generations.
So to sum up, you can think of bear as carrying (an object or offspring) or withstanding something, whereas bare involves exposure (of skin, a nefarious plot, etc).