The button is there, I have empty place slots, so I click it and I end up at the BC upgrades page (I can add contest places though, so it might just be the one button)
This is becuase you HAVE A LOT OF inactive places. It went over the 10 places limit for regular BC. Although you CAN add more places from contests, you need to upgrade to TBC or OBC for more room for active places to show.