As Mushroom25 says, take a train to Manchester Oxford Road. From there, take either a 101 or a 109 bus. (The bus journey takes around three quarters of an hour). Allow about 1 hour 20 minutes for the whole journey.
You can get a bus from Bolton bus station straight through to Manchester piccadilly bus station.
The number 36 goes frequently from stand P in Bolton station through to Manchester piccadilly.
There my be other buses that do this, but Im only familiar with the number 36
From Piccadilly station the number 109 will drop you off outside Wythenshawe hospital.
I needed this info myself last summer, but luckily I got lifts in car instead.