How you account for this depends on who really purchased the share. If the business paid from company funds, it isn’t equity. It becomes a long-term asset, in the same way a deposit with a supplier is an asset. Eventually, you will get it back (at business windup).
If you paid personally, is the membership associated only with this account? Or does the membership entitle you to open many accounts, with this business account being one? (You mentioned “all my accounts.”) In that case, I wouldn’t consider the $1 a business transaction at all. You, as an individual, belong to the CU. The fact that you take advantage of that membership to get a free business account is immaterial in the business’ accounting records. You might just as easily keep all that money in your left front pocket as a petty cash fund. You could close the business account but keep personal accounts open, and the $1 would not be returned.
If you you personally bought the business a membership (which can’t happen at many credit unions) you should enter an expense claim, posting the transaction to that long-term asset account I mentioned above. The expense claim will be cleared either automatically to your capital account (if you have one) or by journal entry to owner’s equity, if that’s the way you are set up.
If I were you, I’d try hard to fit the transaction into the mold in my second paragraph. In other words, I’d look for a way to ignore it.