One good way to get there is by train from Exeter to Okehampton (a relatively newly re-opened line). From right outside the station entrance a whole network of bus services runs- timed to connect with trains.
And there is a really good cafe on the station platform. Although it is an unstaffed station the bathrooms are open during cafe opening hours.
The risk of course is that you don't explore Okehampton town itself. There is also cycle hire in Okehampton town.
Another way to get there is train to Plymouth, then frequent bus to Tavistock. Again from Tavistock there are a lot of local bus services radiate out. You do NOT have to walk into Plymouth City Centre to catch that as it also stops at the back of the railway station.
Bus 98 Tavistock to Princetown to Yelverton (also on the #1 route to Plymouth) being one example. If you go up in the morning bus 172 takes you from Tavistock to Princetown, time there including lunch then the early afternoon Bus 98 ex Tavistock takes you on a tour of the moor on it's way back to Yelverton.
Bus fares are still £2 per journey all year, but there is a little know 'Devon Day' Bus ticket (even valid into parts of nearby Cornwall) for £9.50- which is multi-operator and valid all day from start of service.
A benefit of going by bus sometimes is that you get to visit unexpected places like Yelverton (due to changing bus) which you would just otherwise drive straight through.
I have a set of up to date timetable books for Devon, but hey can't put my finger on them this morning. But this is the County web page for Devon buses- https://www.traveldevon.info/bus/timetables/
Chagford for instance is Bus 173 from Exeter 5 times a day- some extended to Moretonhampstead, 1 hour journey, and the 359 is the faster bus back to Exeter 6 x a day- to give a round trip.
There are many more options than might be realised.
Hopefully the Devon Bus link will give you the information you need, otherwise do revert back.
Even Widecombe in the Moor has a 4x a day circular sightseeing bus on summer Saturdays (#271) from Newton Abbot railway station (an important station on the very frequent Exeter to Plymouth railway line).
I'm not a tours person- I go to where I want to go to at my pace- not where a tour wants to go to at their pace, but am not aware of day tours from Exeter. I think Plymouth Bus stopped their day tours during Covid and never restarted them.