There is definitely a direct bus from Heathrow to Slough as I have friends living in Slough and got it once or twice. Although that was a few years ago I'd be surprised if the service has stopped. Alternatively you could get a taxi but be prepared to pay 15-20 pounds sterling for a ten minute ride. You'll get the bus from Heathrow central station and it shouldn't take you more than 25 minutes depending on traffic.
Try to arrange a mini-cab to pick you up from Heathrow (if you don't know a number just pick one off yell.co.uk - i'm sure there's a few in Slough)
Problem with getting a black cab to points to the west of Heathrow is that it's outside the taximeter area so they can largely charge you what they like (though I think there's some sort of tariff posted as a guideline) - and they like to charge lots.
Slough isn't far at all - but it would possibly cost you £40 in a black cab ? ... As the others mention getting a local mini cab is the way to go.
Public transport wise there may be a bus - alternatively the Heathrow Connect train to Hayes (there's a bus from the Bus station too) where you can change for a train to Slough.
Yes, there are definitely buses from Heathrow direct to Slough. It takes about 20mins. Fares £1.50 the last time I used it. If you ask at the Central Bus Station information desk right outside the terminal they will tell you which number/platform.