You can use subdomains and even sub-subdomains as your custom link domain in Bitly.
When using a subdomain configured with DNS A Records, you will need to update the A Records to point to 67.199.248.12 and 67.199.248.13. If you are using a subdomain configured with a CNAME in your DNS record, you will not need to update anything.
You can check if your subdomain is configured correctly by visiting your Bitly Advanced Settings.