Most hosting providers allow multiple A Records to be configured. If your custom domain's DNS settings only have one A Record, you can add a second one.
Steps vary by domain hosting provider. Find your provider on our list and follow the link to their configuration steps. Then, make sure that you have two A Records that point to Bitly's IP addresses:
RECORD TYPE | HOSTNAME | POINTS TO |
A | @ | 67.199.248.12 |
A | @ | 67.199.248.13 |