The key is your approach, Turtles aren't built for fast getaways, but they are way faster then you'll ever swim. Chasing them is pointless photographically, and bad for you and the Turtle, -you can lose the boat, your buddy, your plan, and end up with butt shots of a scared fleeing animal. What you want is a turtle resting on the bottom, eating a sponge, or otherwise engaged.
Ideally you spot them from a distance, and work your way to them slowly, indirectly, and very low on the reef. Many photographers will use an old spearfishing trick by avoiding direct eye contact. A few other tricks are to pause as you get close, maybe 5-10 feet away, to let them get used to you.
Your bubbles are explosive sounding, so make sure your first exhalation or two are while you are paused, and at a distance.
At about 3-5 feet decide if you are going to hover, or if there is a safe hand hold, if a minute has passed by during this you aren't rushing. When you raise the housing to your eye, hold very still and take your first frame assuming it will be your only chance. If you have approached well, She will keep doing whatever she was when you spotted her.
From 3 feet in (subject to camera distance) and closer with a super wide lens is a magic combination for big turtles- you can shoot every few seconds or so and may find that after the first flash they look up at you. This is when they will often notice their reflection in the dome port, giving you perfect eye contact. After a moment or two, push away and slowly back off- if you have done everything right, she is back to her business.