The additional network cost included in your invoice total covers the cost of BitPay's UTXO sweep for your payment. You can learn more about the reasons for this additional fee here: https://blog.bitpay.com/network-costs/
We recommend that you send a miner fee with your bitcoin payment. Miner fees are given to the bitcoin "miner" (specialized hardware that processes transactions on the Bitcoin network) that appends the transaction to the Bitcoin blockchain. These miner fees are not BitPay fees, but they do increase the likelihood that your transaction will confirm on the Bitcoin network in less time.
A simple way to ensure that your transaction includes an appropriate fee is to adjust your bitcoin wallet settings to include a dynamically-calculated fee. Our bitcoin wallet BitPay includes this setting option, which will help ensure that your transaction confirms normally even at times of high Bitcoin network traffic.
You can find more information about bitcoin miner fees here: https://en.bitcoin.it/wiki/Transaction_fees