Setting a DNS A record and Primary Server Hostname

I want to set the A record for a domain that I own so that it points to a bit.ly server. This is so they can host my url shortener.

I have followed their instructions (see below) and their FAQ to the best of my ability, but to no avail. I realize that this is a specific problem, but I do think it could clarify some issues people may have in similar situations.

Any help?