I’ve heard it can work OK if just one of you swaps head for foot. 
This is a thread about sleeping.
Once the parents have gone to sleep, it’s up on the foot of the bed for me …
First time my husband and I slept together, I was on his left when he was on his back. But when we bought our first house together (about 4 months after we got married), for whatever reason, we changed sides, and that’s the way it’s been ever since.
Even when he’s away, like this week while he’s visiting his folks in Florida, I don’t sleep on his side, even tho it’s closer to the bathroom.
I have no idea how it would work. I’ve never slept with anyone. :o
If we’re staying in a hotel, I pretty much always sleep on the side that has the clock. Otherwise, if the room we’re in has a side that is colder (facing an a/c unit or a vent or whatnot), I’m probably going to be on that side. And the ultimate tie-breaker is that I tend to get the side closest to the bathroom. 
I always took the side harder to get out of or closest to the draft/AC. Growing up my bed was often tucked against a wall or under the slant of the roof so stuff like that doesn’t disturb me at all.
Is it always a side? For me, I prefer to sleep facing away from the center. So when I’m alone, sometimes I sleep on my right side on the right side, sometimes on my left on the left side, sometimes on my back in the middle. I don’t have a distinct preference for which side.
Similarly, I had an ex who didn’t have a side, but rather a philosophy that the man was supposed to sleep closer to the door, the reason being that if there was an intruder I could protect her. This meant one side at her place and a different side at mine.
Anyway to the OP, this isn’t something I really ever put much thought into when I was seeing someone, it just kind of went whatever way it did. Hell, I can only recall that ex particularly because she made a point of explaining it to me when I happened to subverted her preference at one point, and since I didn’t care I obliged. I think, if it’s important to you, settle out that way, if she has a problem with it, she’ll say or do something, and if it doesn’t…well, won’t the fact that you’re sleeping next to someone when that isn’t normal for you be enough to make things “weird” in the same sort of way as not sleeping at home because it’s different?
IMO, if you’re really concerned about it, practice sleeping on both sides of the bed in a few different positions. And, frankly, if you NEED to see your alarm clock to fall asleep, you might want to break that habit. I can see mine from where I sleep, but any time I really notice it, I find it distracting. Either I’m thinking about how much time I have left or how little.
Men sleep on the left side of the bed, women on the right side. I don’t know why this is, but it’s always true. If you think you do it differently you’re just looking in the wrong direction.
My side is whichever is farther from the bedroom door/the bathroom. When she gets up the night and has to pee, she really has to pee. To my knowledge, an extra ten feet makes no difference, but that’s how she likes it.
At the moment, that puts her on my right, and it’s fine with me. If I was with some hypothetical future person, I’d let her pick and take the other side.
If I had to pick a side, I prefer things when she’s on my left. That way, I can roll over on my left side and have my right hand free to feel her up. When I’m alone, I sleep sprawled all over in the middle, so the issue of a side doesn’t really apply then.