hi I know southall really well as I grew up in hayes.
southall is a long way on the bus from shepherds bush, the route may say so and so time but that uxbdrige road suffers long delays at times and you will be sat on that bus for ages.
if you do this get the 607 it is an express stop bus so will be quicker however it doesnt stop at many stops so make sure you get off when it does stop in southall or you may find yourself fast heading for the hayes by pass!
it is on the line from paddington and would most likely be the quickest way, you then have to walk down a straight road for about 10 mins or hop on a bus heading that way for a few stops.
like lots of places in the london area please be aware of your surroundings etc as southall can suffer with some problems.
having grown up in hayes it sure isnt what it was years aogo..then an average surburban area but thanks to dumped large amounts of asylum seekers it can be a bit of a danger and that spills out to other areas.
I get so upset seeing what the area has become these days :( but southall has lots of asian shops and is very busy!!
have fun!