In my "Irish on Your Own" I find the following:

Ar mhaith leat a dhul chuig dráma liom?

Earlier I find:

Cá bhfuil tú ag dul?

Can someone talk about the difference between "ag dul" and "a dhul"?

Does it have something to do with present tense and using the verbal noun and the present tense to reference a future event?

Paul, a chara,

There was a fairly comprehensive discussion on this topic recently. Click herefor details.

"Ar mhaith leat a dhul chuig dráma liom?"

I never saw this form (a dhul) but if it is in a book I guess it's correct.
I would say "Ar mhaith leat dul chuig dráma liom?"

It's a form used to describe what you actually like doing or being, rather than just a general interest in something.

Is maith liom a dhul ag síul - I like to go walking.
Is maith liom a bheith ag scríobh - I like to be writing.

Is that any help?

Actually, the form written "a dhul" is a standardization of the Connaught and Donegal form of the verbal noun of "to go" > a ghoil (Connaught), a ghabháil (Donegal). Actually, "dul" is only used in Munster and "a dhul" isn't used there. So, they tried to find a middle way between the Standard (and Munster) form "dul" and the Connaught and Donegal pronounciation /э γo(:)l'/. But etymologically it's wrong.
Anyway.

Every time u have the verbal noun of "to go", you get "a ghoil" in Connaught and "a ghabháil" in Donegal, except after the preposition "ag" > ag goil, ag gabháil. The form with "ag + verbal noun" is only used when you have the verb "to be" (tá etc) before it. English speakers often have a hard time understanding that since they think they use "ag + verbal noun" every time they have an English verb with the -ing ending. Which isn't true at all. There are many cases in which you'd use the -ing form in English, much more than cases in which you'd use "ag + verbal noun" in Irish.

Ex: is maith liom a ghabháil a shiúl.
Bhí orm a ghabháil chun na scoile.
Roimh a ghabháil chun na bhaile domh.
D’éirigh mé go luath le (a) ghabháil chun na hoifige.

In Donegal, you have the same phenomenon (always a+séimhiú except after "ag") with the verb to come (a theacht) and "to be" (a bheith).

A chairde,
Go raibh maith agaibh.