Usually, a person would just take it without coverings and put it in their own basket or something similar. Pies would also be medieval fast food as the pie shell is a tasteless near-unedible wrapper for the meat and veggies inside.
Depending on the area, because bakers were heavily restricted in how much flour they could use with bread quotas, bread and pies would usually be handed out to people based on their occupation to be charged by the Lord at the end of a tax period. Travelers could also purchase food but the baker had to record it to make sure the Lord is given proper taxes.
She would be allotted bread if she paid for it with the little bit she had or got a job to receive a payment in goods or coin. Bread was also dried a lot of times to allow the ability to cook in soup later.
Which cold bread would have a hard crust during that time period so it would have a "protective coating" so it can be eaten later or throughout the day.