I like that you’ve mentioned in your question that a blunt 'sorry, I have a girlfriend' is presumptuous because my suggestion will make you sound so as well, that’s why I suggest keeping it light-hearted and even making fun of your presumptuousness as well!
I suggest that you are open and honest with your friend. When you get the request, or even when yous are organising where and when to go out, raise your concerns with them in an honest but light-hearted way.
To give you a better idea of what I mean here is what I would say in the same circumstance:
Hey Jessica, yeah of course I’d love to come out for some food, I know
some great places we can try if you don’t have anywhere specific in
mind. I have one rule though, and I know this is presumptuous but I
have to bring it up because it has happened in the past (more than
once):
You’re not allowed to fall in love with me.
I know, I know, it sounds ridiculous now but if we go out for a meal,
just the 2 of us, there might be a candle on the table, we’ll probably
gaze into each other’s eyes once or twice (or at least look at each other), there may even be some soft music playing and there will be a very strong urge to fall in love and make lots and lots of beautiful babies together.
I just want to make sure you know
from the outset that I’m in a committed relationship with Heather and
that we can’t act on this urge, no matter how strong or overpowering
it becomes.
Of course I’m not suggesting you say this verbatim (especially if your girlfriend’s name is not Heather) but if you do decide to go with it of course adjust it to suit you and your friend’s humour / personality.
Now, why do I think this is a good approach? A raft of reasons!
- Zero lying to your friends.
- It doesn’t shift any ‘blame’ onto your girlfriend (if you say you’ll invite her, but don’t, then your friend may incorrectly get the impression she is rude / isn’t interested in meeting them or doesn’t consider you or your friends important).
- Similarly you’re not ‘accusing’ or giving the impression of your girlfriend of anything (like being insecure / overly possessive).
- You aren’t forcing your girlfriend to ‘be the bad guy’ by inviting her when you know she will refuse. (If she is the ‘shut-in’ type she’ll probably appreciate this, but be sure to still offer the invite if it is cool with your friend as well but emphasise that it is fine if she doesn’t as well.)
- You aren’t just inviting other people out to the meal without discussing it. (This is an important one for me because if I’m catching up with a friend then perhaps there are things I want to discuss that I don’t want other people to hear! Hell, maybe I want to discuss your girlfriend!)
- You give them the chance to suggest she comes out as well.
- You set yourself up for something fun and interesting to talk about over dinner. (Just how often do people make a pass at you that you need to pre-warn people? What happened last time? How does your girlfriend react? Have you ever been tempted? Was it Jenny, that ho-bag!?)
- You aren’t artificially limiting your night to a 9pm curfew (which sounds super lame!)
- If it later turns out that your concerns were justified and your friend does make a pass at you then you have an escape route ready that saves both of your embarrassment:
Damn it Jessica! I told you no falling in love with me! You’ve broken
the one rule I have!!! (Then bring it down to a more serious ‘You are
great but things are really serious with Heather and I could never
jeopardise that, not even for one night of fun…’ hopefully that would
let you keep your friendship and not have too much red faces the next
day.)
What I really like about this is it doesn't even have to be just your female friends you use it on!
You could just as easily go through the same spiel with your male friends, warning them off falling in love with you, letting them know you are seeing someone, a little humble brag about past admirers who have tried their luck.
It's a fun little ditty that will roll off the tongue once used a few times. Andddd when it does you can even tell your girlfriend you tell it to everyone you go out with. It can become an 'in-joke' so when your girlfriend does meet your friends she has something easy to bring up (again being the un-socialising type she might appreciate this) 'Did he give you the spiel?' ('What spiel?') 'The one about falling in love! You're such an ass Omegastick, not everyone you go to dinner with will instantly be swooning in your arms!'
(Btw, I love Japan and am planning to visit there in a few years with my wife and kids, if we don't meet up and have this exact conversation I'm going to be very disappointed)