BitPay builds the BitPay and Copay wallet on top of [Bitcore](https://bitcore.io). Bitcore uses the official bitcoind `estimatefee` algorithm to suggest transactions fees. Bitcore evaluates the current Bitcoin network status and the urgency with which the user wants her transaction confirmed.
If you’re still curious about how we calculate our miner fees, you can check out our code for yourself. It's completely open source.