I would be cautious about writing a note if I were you, what if he has a girlfriend and she picks up the note. He might have a girlfriend that does not even live with him but happens to be around when you slip it under. Now odds are he's single, but I think it would be easier & safer for you to ask him in person. Don't worry you have to go pretty far before a guy thinks your desperate, most men are flattered by the thought even if they can't if they are already with someone. A note might go down ok and if your reasonably sure he's single (though sometimes someone looks single then you find out after ages they are with someone) then sure go for it, he will probably find it ok but I think can come across a bit weird or create a weird situation, a knock back is probably easier in person than a weird conversation over - did you put this note through my door, or no reply then seeing each other. Instead next time you bump into him could just hang out a question like does he know where a local bar is as your at a loose end/bored/wish to kill some time as your in your flat by yourself, then judging on perceived atmostphere (he may just be nervous which is ok) just gently enquire if he would like to come too, i.e he might be bored also/alone, etc but ask him if he would like to go to bar first, not whether he is alone as he might not know what you are driving at. So perhaps think of this as another course of action instead. To come across desperate to a guy you basically have to throw yourself at him in a very direct perhaps even sexual way, I think it rare for females to come across as desperate, its almost always a perceived fear, men nearly always welcome the interest and are relieved they don't have to do all the work for once. Just go for it.