Public transport is all good. It's not far out of the city of Wolverhampton; and it's located on the main road into Bridgnorth. There's information on the National Trust page:
http://www.nationaltrust.org.uk/wightwick-manor/how-to-get-here/ If it's a clement day, then it's not a bad walk up the canal from Wolverhampton city centre. That's a few miles though, so only for the fit and hail!
Otherwise the 890 bus from Wolverhampton to Bridgnorth will pass outside it.