hey, so she is like 31 or what?
You 23 and her 27? For me it's just normal age difference.
So..
you woke me up
_what_? you leave you cellphone on at night?
OR: So your sleep is really light. didn't know.
if she then pushes it, someting like
"I misjudged you. Obviously it was not on purpose, and you make a big deal out of it?"
Just change your frame or mindset slightly. Nothing awkward here, and quite understandable if people wake up in the middle of the night they are not too happy about it. She could have turned her phone off, you could have choosen a better time. That' it.
Next again, just sell the "no girlfirend thing" differently on a second date. "I like no strings attached until I find the right girl (otherwise it's a waste of time)".
So have fun on a second date then
(and yes, English is not my first language, those are just hints...)