What if you're not given an option for a transaction fee? I purchased some Bitcoin through a local bitcoin ATM. When I purchased the Bitcoins I was not given an option to ad a transaction fee and currently it sits unconfirmed.

I also have a app on my iPhone that I have just started using to manage my Bitcoin called Bitwallet and in its 'Pay' screen it also does not offer an option to include a fee.

What are you meant to do to confirm transactions if no option for a transaction fee is ever offered?
As Nick says, there really isn't anything you can do by yourself. The transaction fee has to be included when the sender creates the transaction.

There is a provision for transactions to be confirmed without fee, based on a "priority" measure that depends on  the size of the transaction, and the length of time since those coins were previously spent. As such, the priority increases over time, so the transaction should eventually be confirmed, though the length of time depends on the size of the transaction. (The size may be larger than the amount due to you, if it includes payments to other people or  an amount being returned as "change".) If you have the transaction ID, you can look it up on a block explorer like blockchain.info  and see the priority.

If it doesn't confirm in a reasonable length of time, all you can do is take it up with the ATM operator. In principle, they can try to retract an unconfirmed transaction (by double spending) and issue a replacement or a refund.