And, okay, on re-reading your post, that standard answer may not be on target. If the "bullets" you are referring to are just inline characters, you can only change them with the find/change process you're already using.
I would create a Character Style for them, and assign it using Find/Replace. Set F/R to "GREP."
For 'Find," cut and paste one bullet into the field, so that there's no guessing which glyph might be in play. (If appropriate, set Find to "BODY" text or whatever Paragraph Style holds this text, to limit it to that text alone.} (The standard code for a round bullet is ^8, by the way, and in GREP, it's ~8.)
In Replace, you can paste the bullet again, or use the "Found Text" code, $0. (The latter will put the same character in; you could also substitute another character if you like.) Click the T/magnifier icon and set it to the new Bullet character style.
Run Change All. All of your inline bullets will now be assigned the Character Style, and you should be able to tweak it to your heart's content. (Pro tip: make it bright magenta or such, and review to make sure all the bullets are so tagged. Manually tag or fix any that got missed, for whatever reason. Then set the Character Style color to whatever it should be.)