It's possible to get the X31 bus to ZSL Whipsnade from Luton Train station (on the main Brighton-London St. Pancras-Bedford/Leicester/Sheffield line). It goes via Dunstable and Hemel Hempstead, but buses to the zoo only call there every two hours. I believe the buses run every hour in the high season, but don’t quote me on that. I can’t say how good the service is though as I’ve not yet tried it out yet, but hope to soon.
I normally travel to Whipsnade via this bus seven or eight times annually; generally I have found this bus service very reliable.
However, unless the timetable has been changed recently, buses to the zoo only run two-hourly even in high season. It should also be noted that, unfortunately, this bus does not operate on Sundays or Bank Holidays.
I normally board the bus outside Hemel Hempstead railway station; the journey from Hemel Hempstead to Whipsnade goes through some very attractive countryside making a much more pleasant bus ride than travelling in the other direction from Luton to Whipsade.