"Kittie's mission - find Grace a guy that's got that,
just got out of bed tossed, good looks kind of thing going on."
You can get tossed out of bed, for instance when you are thrown out of bed. So "tossed" (from the verb "to toss") is an informal, colloquial way to express "getting up"...
On a whole, the expression you're trying to understand is humoristic, referring to a person who even looks good when tossed out of bed, or when awoken suddenly, a person who even looks good with a sleepy head...
Hope this helps!
Thomas (not a teach)