Yeah, same here except I can't board a transport ship at all. I was only able to board a transport ship by having my units garrisoned in town and then clicking on the ship. If they are not garrisoned, I can't load them onto a ship at all.

I've only built one boat, so this is something I haven't tested over and over again...

I had four soldiers, a frigate, and my sovereign in a city.  I tried to move them all out into the ocean.  Only the soldiers and frigate moved out.  I couldn't get the sovereign to board the boat.  I tried unloading the soldiers first, and then getting the sovereign to enter.  I tried going back into the city, going onto a beach tile...couldn't get the sovereign on board at all.