I'm going to assume your hobby email uses a false name and your email is not linked to anything, and same goes with the provider you mentioned.

I used G+ a few times but discontinued use.
Things may have changed since then, but no one in her circle will see your profile or email, especially since you have not accepted her request.

and even Linkedin, believe it or not.

I just ignore them all, and so far nothing untoward has occurred.

You'd have to be changing your email three times a year eventually, and I agree that it's just a big PITA.

Stay with your current email and just ignore the requests to join.

The hobby and on-line social network sites are a very bad mix.

She probably didn't invite you anyway. Those sites "mine" people's computers for contacts and send out invites. so basically she may have joined using her provider email addy, and it just sent out blanket invites to everyone in her address book.

which is it's purpose after all...  just ignore it.   Yes, I get them too.

And if this is really nothing more than a hobby email, who cares?

I had a similar invite from a provider I like and see regularly.  The invite came to my hobbying email but I still didn't fee comfortable signing up.  I started cliking on various persons in the circle of friends and the ever expanding circle could I think lead to some over exposure.  Plus when I tried to sign up using a fairly obvious pseudonymn, I got a message saying that Google discourages that sort of thing.  In short I have a lot to loose and not much to gain.  If I were you I'd avoid it like the plague.

She opened up her entire contact list for google to now send out a mailer to anyone on it, asking them to join. Again, stupid! If I were you, I would close the account and start over. Tell your refs from this account you are changing it to such and such so they know you're the one sending the email, and they can still vouch for you.

First of all, you probably got that invitation just because you both had exchanged email in the past, when she joined Google+ it probably auto-invited anyone she had sent email to on gmail.

Secondly, I would get a new hobby email just to stop using gmail.  There's way too high a chance of something in the Google system tying something else to your email in unexpected ways - like for instance using your hobby gmail, then clicking on any page with Google Ads on them after.  Probably nothing would come of it but Google at some point would probably gather enough data links to connect the real you in some way back to the hobby email.

A hobby email should probably always be on a system you don't normally use for email - Hotmail, Yahoo Mail, or some other free email service.