Why does my dog keep 'bowing' all the time?

Yeah, same here. I’ve always just seen it as a stretch, sometimes accompanied by a massive yawn. There’s a real difference between that and an invitation to play, where you can clearly see she wants to play because she gets all excited as well.

I get those back leg stretches too, sometimes while she’s getting off the bed, which looks pretty weird lol (both front paws on the floor, one back leg hovering in mid-air and the other still on the bed). She arches her back like a cat, then lifts her head and stretches her neck...

Mine does it too every time we go out, when I crouch down to put her lead on, and sometimes when I call her over to me.

"I'm treated to that every morning, followed by a back leg stretch" – in that case, he’s simply stretching.

These two stretches are actually what gave their names to two of the most famous yoga poses: downward-facing dog and upward-facing dog.

On the other hand, when he does it during the day, it can also be a "calming signal".

In my opinion, since you’ve got a very boisterous young dog who finds it hard to settle and you’re spending a lot of time training him, it would make perfect sense for him to use this posture when he’s being asked for a bit too much.

When my girl was younger, she used to do these massive yawns during our obedience sessions... She had so much energy that even a few minutes of concentration required a huge effort from her. Even today, when I'm teaching her something new, there’s a phase where she yawns a lot because she’s not entirely sure what I’m asking of her.

Anyway, those are just examples of situations where your dog might be using that pose as a calming signal.

No, I don't think he's asking me to play because when he's in that pose his tail doesn't wag, and sometimes when he does it he just 'flops' down into a lying position

That’s definitely a play bow.

Mine does that quite often too. It seems like an "invitation" to come and play with him or just to get my attention.