Everyone is on the "the bride is a shitty friend" train, but I'm not.

I'm guessing the people who got +1's are in steady relationships - they were not an open invitation. Generally speaking, you extend a +1 if someone is in a serious relationship, but it is not a necessity if someone is on their own. It's a courtesy, not a given. It's also not a statement of "forever alone," it's logistics, and generally accepted practice.

Also - if the wedding is a week away, have you not already RSVP'd? This isn't an Evite or a Facebook Event where you can just say "yeah, I'm bringing someone." RSVP's for formal events are so you can finalize the catering. If you RSVP'd for yourself, then that's how that works - you RSVP'd for yourself, without your new girlfriend. That is what the bride planned for with seating arrangements and head count.

You are within your rights to not go, but a wedding is an expensive event to issue an open-ended invite to you that you may or may not have brought a date along for. (And I say that as someone who was the last of my friends to get married - I went to a LOT of weddings alone, including as a member of the bridal party.)

If this relationship accelerated in seriousness so quickly, you should have contacted your friend earlier and asked if there was still room for you to bring a date. One of our oldest family friends didn't realize I'd gotten engaged before they mailed out the invites daughter's wedding, and we called and asked if my now-fiancé could be invited, or would that mess up the plans? (They were fine with it since it was one of the first RSVP's they received.)

You really should just chalk this up to one of those social engagements that happens early on in a relationship - you've already committed to go as a single and sometimes you have to separate for a night to be a polite guest. It's awkward, obviously, but if your invite didn't say "Yawaworht077 & Guest" then that was the terms on which you agreed to attend the reception.

Now, as a practical alternative - if there's a cocktail period or something, can you ask the bride if you can attend that with your SO and then leave? Cocktails and appetizers are less formal than dinner, so that wouldn't throw the food off that much. You can see the ceremony, you can congratulate her, and then finish your evening elsewhere.