There are a few different character limits in Bitly:
We can shorten URLs up to 2,048 characters in length. This includes all punctuation.
This limit applies to links you use for QR Codes and buttons on your Link-in-bio page, too.
The maximum length for a custom domain is 32 characters, including the dot.
The character limit for a custom back-half is 255 characters. Visit What characters are supported when customizing links? to check which characters are allowed.