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The TTL (time to live) in your DNS settings can be left at your domain provider's default settings. The TTL should not affect your Bitly usage.
GoDaddy has a great summary of TTL:
TTL is the amount of time servers cache the information for your DNS records. For example, if you set the TTL for a particular record to one hour, servers store the information for that record locally for an hour before retrieving updated information from your nameservers.