It didn't occur to him to apologize so much as wait for her to regain her composure. Dean often told him not to simply turn up when people least expected him to, but Castiel didn't know any other way. As for the oxygen tank, he didn't know if it was really helping her or not. Whatever was afflicting her was aggressive.
"Thus far, that seems to be the theory," he agreed, nodding. "Though technically we've not lost and received anyone for that assumption to be true either."
She introduced herself, which to him signaled that she was attempting to at least be polite. He didn't know what else to do, so he decided to do the same. "Castiel. It is...pleasant to meet you. Or it would be, if we had any understanding of why this is happening."