Is that square a Wingdings or dingbat? If so, you can include it and the Right Indent code inselfin a Lookbehind, like this:
(?<=~yX ).+$
— I put an 'X' where you should paste the dingbat. Note I added a space after the “X” as well, as per your sample — that way you always need a space between the dingbat and the following text.
If you are using different dingbats, you could use the 'any' wildcard:
(?<=~y. ).+$
as it does roughly the same: after a Right Indent and any character at all, apply your character style up to the end of the paragraph. If possible use the first one, because this one will also pick up a stray space that might have crept in right after that Right Indent, and then the bolding is done on everything after that.
This is for a signature so I can't target the end of the paragraph (because I want to use the same paragraph style for the last paragraph as others).
As it is, my first suggestion will only be applied to Some more text in the exact sequence “Right Indent — Dingbat — Space — Some more text — End of the line”, and it will ignore every paragraph where this does not occur. So it's quite safe, I'd say.