You can easily add your Copay-hosted wallet to BitPay by restoring your wallet backup in the BitPay app.
If you have a wallet seed phrase, go to Add Wallet > Import Wallet > Wallet Recovery Phrase in the BitPay app and write down your 12-word Copay backup.
If you've backed up your wallet in a file or text block, go to Add Wallet > Import Wallet > File/Text Backup in the BitPay app and upload your Copay text or file backup.
Note that you will now be able to view the same wallet in both Copay and the BitPay app. Changes made to the wallet in one app will be reflected in the other.
If you have notifications enabled, be sure to disable them in one of your apps to avoid duplicate notifications. You can also delete a wallet from your Copay device (after you have imported it into BitPay) by going to Wallet Preferences > Advanced and selecting "Delete Wallet."