As an adjective, bare means lacking clothing, naked, exposed to view, or lacking adornment. As a verb, it means to make bare, to uncover, or to expose. Its past tense is bared.
Bear has no adjectival definition. When not referring to the large mammal, it is a verb with a variety of meanings, none of which relate to uncovering or exposing. A few of its meanings are to hold, to support, to exhibit, to carry oneself in a specified way, to endure, to give birth to, and to yield (especially fruit). Its past tense is bore (e.g., it bore fruit), and its past participle is borne (e.g., it has borne fruit).
So bear is the correct spelling in the phrasal verbs bear down, bear out, and bear up. It’s also the correct word in the phrases bear down on, bear fruit, bear in mind, and bring to bear and in the common phrases grin and bear it and bear the brunt of. Bare wouldn’t make sense in any of these phrases or expressions.
Bearing in mind that the verb bare always means to uncover or expose, consider whether these sentences make sense:
One roof collapsed in Naugatuck and several were evacuated as the heavy snow proved to be too heavy to bare. [WTNH]
Many a gardener wish they had fruit trees old enough to bare fruit in their yard. [Canada.com]
Obviously, these writers mean bear instead of bare.
And here are a few positive examples of the words in action:
SAC will bear the brunt of any costs arising from the probe. [New York Post]
Blowing and drifting snow and cold temperatures continued to make it difficult for any of the snow removers to reach bare pavement. [Champaign/Urbana News-Gazette]
Bear in mind too that other employment indices have been strong. [The Business Insider]
Now, however, the 31-year-old television presenter has agreed to bare all in a confessional internet diary. [Telegraph]
The debate on the House floor came down to the right to bear arms versus the rights of private property owners. [Daily Herald]