Regretfully or regrettably?

[BerylStreep]

If you were sending someone a 'sorry, no' e-mail, would you say regretfully I can't ... or regrettably I can't ...?

I am regretful. It is regrettable.
It depends which one you mean.

Regret I don't think it appropriate to have a meeting with you.

regretfully

Say "I regret that I can't", then you will also avoid the adverb-as-modal-adjunct bear trap. Assuming, of course, that you actually can't, as opposed to not wanting to, and you really do regret it.

Thank you.

It would possibly be more accurate to say 'There's not a chance in hell that I'm going to meet you.'

Unfortunately we are bound by niceties and professionalism.

isn't a particularly well constructed sentence, from a gramatical pov.

Better to say

Thank you Middleagedmother. The e-mail is already sent, but I think I knew it wasn't that well phrased.

I am a complete pedant when it comes to spelling and punctuation, but I could probably do with some refresher classes for grammar.