Yes, by miles, a rental car would be the far best option.
Even if you get a taxi from Chipping Campden and go the most direct way by car it will take at least an hour each way.
I hope the gravestone is in good condition and you are able to find it easily.
Will you do anything else in that area that day? Maybe a ride on a steam train at Kidderminster (Severn Valley Railway, arguably the best preserved railway in the UK, therefore the world) or visit the canal locks at Stourport on Severn, or perhaps Worcester Cathedral or the Grey Friars there?
If you were doing anything else it may help you decide on the best train route or taxi.
There are always plenty of taxis around Kidderminster, which is much closer than Worcester (less traffic for the taxi, too) but as said above you'd better have a taxi wait by the church in Rushock or you will never get another.
That part of the world is really one where having a car will be very helpful.