Hi Tree - just came back to this thread and saw your message.
The bus connection to/from Audley end is very quick, dependent on where you're catching it from it takes between 5-10 minutes to get there. Just be careful getting to the station during the day as there are very few once the morning rush is over, or at weekends. The buses back tend to coencide with the trains arriving and it's rare you have to wait long for one. There are always taxis there too (costs about a fiver) if you need to get back in a rush (I've only had to do that once since we moved here in March).
If you go to the traveline website you can enter Saffron Walden to Audley End station (or vice versa) and it will show you when the buses run.
DD is 5 and just gone in to her second year at school, so we haven't really had much exposure to the toddler activities, but friends who have younger kids (or who are childminders) always seem to be going to stuff at the library. There is a soft play centre just outside of town and another one in Linton (as well as a zoo) which is not far away, although you will need a car to get there. The museum in town often has stuff going on and at weekends Audley End minature railway is an absolute must (they also have a playpark, cafe plus a bouncy castle/swings there in the summer).
I won't lie to you - the reception years in the local primary schools are packed, you should be fine if you're in a catchment area, but I'd seriously take that into consideration when looking for a house and get as close to one as possible. I've heard great things about Katherine Semar, and RA Butler is also good (although has recently lost its OFSTED outstanding status and aparrently "requires improvement"), both are big schools (RAB in particular).
There are 2 VA schools; St Thomas More which is Catholic, and St Mary's which is C of E. DD goes to St Mary's and although I didn't particularly want her to go to a VA school, I've been really impressed with her development since she's been there, and she's in a class of 20 which is amazing! It really is a lovely school.
Hope this helps, and good luck with the move! It really is a lovely place to live.