URL shortening services like bit.ly do not use DNS records, but instead leverage URL redirection to forward a HTTP request, and as this is done through their servers, it potentially exposes you to third party tracking.
(As a a side note: You can test where a bit.ly link would take you by appending a + to the URL, e.g. https://bitly.com/bbZkLH+ for checking https://bitly.com/bbZkLH )
Whitelisting bit.ly does not affect blockage of the target domain:
Pi-hole sees the DNS request to the redirect domain as an additional, separate DNS query and would still be able to block it accordingly.