What type of Corporate card do you have and is it enrolled in Membership Rewards? Not all employers permit this. If it does, have you "linked" your Personal and Corporate card accounts? There is a fee to do this, $75 per year I believe.
The $75 fee is correct. I have a Green card for work that I never use. When I inquired about linking it to my Platinum, they told me it would cost $75. In my case, not worth it because I literally never use my corporate card. But if linking will allow you to take advantage of the transfer bonus it may be worth your while.
Note that there are some transfer fees as well. I think they cap at $60, but worth knowing.