if you have one of the wood cages with the screen the easiest way is to hold the cage down in the hive against some comb and peel the screen off. you can let her walk right onto the comb.
slip a blade under the edge of that screen before you start so that it's easy to grasp and remove. just don't go so far that you open it and let her out.
how long has she been in and are the bees taking care of her? she can stay in a long time as long as they are tending her. i forgot one once for a week. queen was fine.
you don't need good weather....you just need a warm enough day that's not pouring and windy to pop the top and let her out.
if we wait for great weather in the PNW, we don't get much done
where in SW washington are you?