There are several "Stratford"s in the UK.
One is the area in East London where the most recent London Olympics was held and now the location of the strange Mittal sculpture cum thrill ride and many sporting activities, as well as a tourist attraction.
I'm guessing that you actually mean the birthplace of William Shakespeare, which is Stratford-upon-Avon, in Warwickshire.
If so, it is possible to reach Stratford-upon-Avon from Warwick via train in about 35 minutes several times a day (5 stops, direct) or somewhat longer than 90 minutes via Birmingham Moor Street but more frequently. I haven't checked but Saturday service is likely near a weekday service and Sunday service if it exists at all won't be direct and you probably will have to go via Birmingham Moor Street.
I have no idea about tour buses.
Both Warwick and Stratford-upon-Avon are very easy to reach by train from London.