If visiting Sidmouth from Exeter the Stagecoach #52 (A and B) runs about half-hourly during the day and hourly later in the evening with a journey time of about 45 minutes. If making a day of it then the £6.50 "Explorer" ticket is your best buy as this allows unlimited travels on all the company's services around south and mid Devon and so if you fancy enjoying a walk along the coastal path your ticket is valid from any of the destinations either back to Exeter or to Sidmouth.
Sidmouth's main bus stop is at the "Triangle", pretty much in the centre of town and a short walk from the seafront.
Stagecoach Mainline bus routes 52a and 52b run from Exeter Bus Station every half an hour (hourly on Sundays) throughout the day until late evening. The route is quite scenic.
For the Sidmouth seafront, get off the bus at the Sidmouth Triangle.
A day return ticket costs £6.00. This is actually a Stagecoach Devon Day Explorer ticket, so you can use it on any other Stagecoach service that day. For example, we used it to return to Exeter on the Coasthopper route via Exmouth.