How early is your breakfast reservation? Before specific park buses start running, they run "Character Breakfast" buses that stop at the hotels, you tell them where you need to go and they get you there. You might have to make more than one stop, but they'll get you where you need to go, even if it's a hotel.
Your later-in-the-morning option depends on where you're starting from.
If you're at AKL, you could bus to AK and then bus to Beach Club.
If you can conveniently get to the MK via boat or monorail, you could head there and then bus to the Beach Club.
Most other hotels it's probably best to bus to the Studios and then boat or walk to Beach Club.
-Rob