I like this and could see myself using it, but think seconds are not really necessary - it makes it a little harder to read and I'm not exactly going to set my alarm for 06:21:57.

Also, perhaps when pressing 'I know my bed time' the text above should fade/slide out and be replaced by the other section? Something maybe like this: http://i.imgur.com/OZ8t6NI.png

Finally, not sure if it's intentional but good call on going for white on black: sleepti.me does the last thing I want to see when I go to sleep it a glowing white background!