Do Bitly links send your emails to the recipients Spam folder?

I use Bitly links in emails to 1) confirm that the recipient clicked on it, and 2) to track subsequent clicks to gauge their level of interest.

Last week, I sent emails to two new prospective clients with Bitly links to product sample pages included in the body of the emails. Both were first-time emails to these guys. Of the 2 emails, none of the Bitly links were clicked on. Both clients knew in advance the emails would be forthcoming and were ok with that. I'm coming to the conclusion that Bitly links (and other link shorteners) cause the recipient's email clients (Outlook; Gmail, etc) to blacklist them and send them to the spam folder.

Appreciate any feedback to confirm my hunch. T.I.A.