When she called him "boss" it prompted him to shake his head and correct her. "If you have to address me by position, then please use Commander. I'm sure a Captain of your stripe will find it preferable, and it'll set an example for the rest when it comes to public image and professionalism." The way in which he delivered those words was so utterly formal and perfect down to the tone, it sounded authoritative but polite at the same time, but yet when he'd finished saying all of that it was topped off with a casual wink to suggest that while he'd been perfectly serious he wasn't actually offended.
"If you'll consider integrating the ship into the Alliance's structure then I can justify us covering the balance expenditure. This obviously means you'll lose your absolute autonomy as a distinct taskforce, but it does give you access to more resources." This was a purely professional suggestion and something for her to consider as time went on, he expected that she'd take some time to think about it and then eventually get back to him.