I am in English, although I have not reviewed applications for a PhD program. It it those respondents whose advice will likely be the most helpful for you here (if any of the people who have already posted fit that profile, I imagine they will speak up).
So, from my somewhat limited perspective: conferences? Well, if it's MLA, then by all means do it. But if it's just a regional or subfield meeting that wasn't that competitive to get into (very few are, they want all the conference fees they can get), and it's going to cost you hundreds and hundreds of dollars to go? I would skip it. The teaching job, by contrast, will actually *put* money in your bank account.
More importantly, as others have indicated, it will make you a top candidate for a TAship in a PhD program assuming you have gained admission. It also signifies that the Chair of this dept. feels that you are already qualified to be teaching a class on your own.
Lots of undergrads have a conference presentation under their belt. It is certainly a good thing to have, but it does not automatically indicate the brilliance of your work, since lots of people have mediocre, half-cooked research accepted to conferences.
Your writing sample will be far more important and concrete evidence of your potential as a scholar. That is something the Admissions Committee can actually look at. They won't have access to your conference paper.
Last item:
I don't want to agree to teach the course knowing I'll be absent a significant number of times.
I would be very careful about skipping more than one class in a given semester. What is "a significant number?" I believe adjuncts can be docked pay for cancelling any class -- and that also might not be viewed well by the Chair that hired you, unless you make it clear up front that you will need to miss those classes for very important, unavoidable reasons. You don't want to nix your opportunity to get the teaching appointment by being honest, but this is not considered a perfectly acceptable thing to do, especially for a new adjunct.