Rescue orchid growing flower spike in cramped window

[visuallace]

Ok, so I rescued this clearance orchid from the home improvement store maybe 6 months back; it was half rotted and had a couple shriveled flower spikes with no flowers, and 2 or 3 leaves that were at least partially salvageable. I put it in my bathroom windowsill and when it looks dry I water it in the shower. It's really been taking off, lots of new roots and leaves. I've been meaning to put it somewhere else, as it's grown too big now for the narrow window, but I wasn't sure if it would be so happy in another room.

Well, when I took it down to water it today, I saw that it had a flower spike growing on the side that faces the window. I've never had an orchid live to rebloom, and I've got no idea what the flowers on this one even look like. So exciting! But what should I do with it? There's not enough room where it's been sitting for the spike to grow out. The spike was already pressing against the window. Should I find it a bigger window in another room? Put it outside during the day (it's been in the 60s - 70s F here lately)?