Messed up my .bash_profile remotely, can't ssh back in

As described here you can use

ssh -t user@host bash --noprofile

in fact, as @JoL suggests, you don't even need the --noprofile, since when ssh executes bash as just another command, it's not considered a login shell. Running ssh -t user@host bash will only read the RC files; and running ssh -t user@host bash --norc will not read even those.

Try to SSH and run sh instead of bash, e.g.

ssh user@host sh

Then rename (mv) or edit the broken file (ex/vi).

Run ssh -t host vi .bash_profile (or the editor of you choice in place of vi) and fix your .bash_profile.

(The -t option may not be needed, depending on which editor you choose.)

If you know exactly what needs to be fixed, you may be able to fix it non-interactively. For example, something like

printf 's/exec foo/. foo/\nwq\n' ssh host ed .bash_profile