Hi tevion, I don't think it's stupid at all
We moved our dc several months ago to a different infant/junior school. It was really strange going from a school where we knew everyone, to one with 'new people' !
I too feel shy around people I don't know, and it's made a bit harder because most of the children arrive by bus, so there aren't many people around at drop off to chat to.
We also still have playdates with friends from the old school. I don't see it as being odd, I look at it from the point of view that it's always good to have non-school friends. And yes, I'd have to say it is usually me who organises them, but sometimes I think that's just the way things are.
All you can do with regard playdates from school is keep trying. The first mum my never have got the note - lost in the bottomless pit of a schoolboy's bag! The second mum may be even more uncomfortable than you with 'new' people.
Also some people are nervous about going to 'strangers' houses, so maybe try and arrange something at a play place or park?
We've had some people who've never responded, but I've just moved onto the next person, and tried again later.
I also think it's important not to worry too much about the fact that you don't know people. It doesn't matter if you and your son's friends parents don't become friends (although it may happen with time!)
Also remember that it's still very early days, so don't be disheartened.
It really will get better.
I hope this is of some use, or reassurance, even though it's a bit rambly and littered with ""