ATM Basel airport

Here you go:

https://www.euroairport.com/en/passengers-visitors/restaurants-shops-services/services/currency-exchange.html

I hope you are taking the bus into Basel.
Bus: CHF 6.10 per person, including connections to anywhere in Basel
Taxi: ~CHF 40+
Bus stop is just outside the arrivals area. Buy tickets from the machine at the stop, the driver does not sell tickets.

And, when you arrive, after picking up your luggage, make sure you go through the exit on the right marked "Switzerland", not the exit on the left marked "France", or you will end up in the wrong country.
See photo here: http://i.imgur.com/0mVaL7Q.jpg
This is what it means by "sector France" and "sector Switzerland" in the link Lola posted.

Ashley,

To add to what Chris mentioned, be sure that the ATM dispenses CHF and not Euro (I can't recall if the buses accept both currencies). It looks like there are three different bus services from the airport to Basel, and you may be able to buy tickets inside the terminal.

The ATM in the French side of Basel airport will dispense Euros. In the Swiss side Franks; it may have a Euro option (many of the machines in Basel do).

There is only one bus route from Basel airport Swiss side, the No. 50 to Basel station. It runs every 7½ minutes. Other buses leave from the French side to French and German destinations, you will be on the Swiss side (big fence runs along the border).
You cannot buy bus tickets in the terminal, only from the ticket machines at the bus stop. These, like all ticket machines in Basel, take Franks and Euros.
This is a photo of the bus stop at the airport: https://files.newsnetz.ch/story/1/6/7/16751284/8/topelement.jpg
You can see the ticket machines on the right, under the blue sign "Tickets to Basel".