So I got my free shuttle from Admiral T'nae but need some help switching between flying the shuttle and flying the ship.
I got on this morning and was mysteriously flying the shuttle. Not sure how. Now I can't figure out how to get back. I've tried visiting the ship selector in the shuttle bridge but all that lets me do is select a ship, when I leave I'm still in the shuttle. Same was true when I visited the small craft selector in the ship.
You don't have to go back to a starbase, you've got a ship selector at your fingertips. click the down arrow at the corner of the minimap, and go either to your bridge or your shuttle bridge.
On both (right in the cockpit for the shuttle, for the ship bridge you'll have to take a turbolift to the engineering deck and find the officer in the transporter room - obviously shuttle bridge is more convenient) is a ship selection officer who's limited to your current default ship and all your shuttles. You can switch into or out of shuttles or change your default shuttle from here.
Only time you have to go back to base is to switch your primary ship.