There are a few different character limits in Bitly.
Long URLs
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 Bitly Pages, too.
Short links
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.
Custom domains
The maximum length for a custom domain is 32 characters, including the dot.