It's over politically-correct to say "you cannot do it" or "you have to ask permission".
When commuting I find that "drafting" sort of happens naturally or by accident.
This type of "drafting" is very different from racing drafting. You cannot be safe and draft at speed right on the wheel of someone you don't know! It is more like companionable cycling, there has to be alot of awareness (preferably by both riders) and you have to anticipate and give a lot of space.
Asking for permission doesn't make sense . . .
I find that it's not really that possible to chat / ask permission as "drafting" will start by accident when a rider slightly faster than another overtakes and the overtaken person can then keep up and draft. Mostly there is a difference in ability and the overtaken is not able to speed up and take turn in front. You are sort of stuck as due to benefit of draft you can keep up, this is your natural pace and even if you drop your natural pace off you might well be together again at next set of traffic lights.
If I catch up with someone and realise we are going the same speed more or less then that's a tricky one. I can stay behind. Or I could try to overtake but I think this might be a bit rude if the speed difference is not big and you are probably going to not be able to pull away clear of them.
There's a long steady uphill section on my commute home mostly with mixed on-road and shared foot/cycle path. I often find I'm riding at the same pace as other cyclists so drafting happens somewhat naturally. I don't find that taking turns happens at all much. Especially, of late, when the cyclist in front is on an ebike! :-)
I don't think it makes sense to ask for permission in this situation as all that is happening already is you are travelling at the same space. If permission is granted or denied then what are you going to do? You might be accidentally together for a while anyway!
Is it rude ?
I don't think it is rude ...
Communication is good . . . leave the other cyclist know you are there.
Yes, a bit of communication would ensure it is not rude.
I do try communicate alot on the road. (using traffic signals and voice)
I think I'm a bit shy communicating with other cyclists if moving at a good pace. I would be more concentrating on riding.
You might exchange a word if you stop at traffic lights.
In commuting you don't say hello to everyone who passes(maybe that would be nice! :)). Also, by the time someone has overtaken and you realise you are comfortable in draft your moment to say hello is sort of passed.
Hmm. I could try out something like, "oh, I seem to be behind you now, er, hope that's ok. I'll be careful."
Hmm, well actually, thinking about it, I'm not too bad really, in front or behind I call out hazards, intentions and signals I'm making. Hopefully not too disconcerting for the other cyclists.
Most cyclists do not mind?
I said before something like "Depending on relative speed and road situation common sense prevails.". However I think I was wrong. As pointed out elsewhere people think differently. My common sense might not be the same as yours. SOLUTION: Communicate!
Sometimes someone would overtake me or I would catch up behind but think it doesn't make sense to overtake here . . and I end up cycling behind someone. And it is a bit unclear if they are aware of me or not.
A bit awkward but I guess safer and less rude if communication happens.
I like to drive/cycle defensively and find I generally have good awareness of riders or any traffic ahead and behind of me . . so I think that makes me more comfortable with someone tagging along sometimes.
This "drafting" is not like racing bike drafting.
I find riding as a pair like this is better for safety against car traffic.
If in behind someone assume they are not as aware or might be less experienced. So you have to be vigilant to hazards ahead (and behind) and anticipate for both of you!
If ahead of someone (OR even if you think you are alone!) similar applies. Always communicate and signal to that imaginary rider/car/other behind that may or may not be there.
Defensive riding techniques apply as always.
you have to be HYPER-aware of what is coming up in front as well as road situation all around/behind
you cannot draft right on wheel expecting signals as in road racing. It is an informal arrangement! (there is still good drafting benefit and more safety a bit back and off to the side)
When drafting like this I try to be of safety BENEFIT to the cyclist in front.
You can back off frequently and give space as the cyclist in front encounters hazards, make it clear you are not going for overtake and making space for them to do so.
move to the side to look in front and behind, (be careful to try and not block the view of the front rider if they look behind)
signal to front and behind and look after both yourself and others.
voice call out hazards, intentions and signals you are making
safety check and signal and claim the road lane early if it looks like you have to move out to avoid hazard/overtake/...
I generally have flashing lights on and I have a bell too :-)
Bells . .
I don't know is this just Dublin, Ireland, but many cyclists don't have(illegal here) or use bells. I find the tinkle of a bell + voice from well back mostly gives good enough warning to pedestrians/dog walkers/other hazards(:-)). Warning enough that multiple cyclists can pass in a friendly way as opposed to all coming to a grumpy slow halt or blazing past close by in a dangerous manner.