The only real option, unless someone can give you a lift, is a train into London and back out:

http://traintimes.org.uk/wareham/ssd/14:00a/2011-07-10

The other option is if someone else is going back to Heathrow on the Sunday you could get a lift and then a transfer to Stansted by coach:

http://www.nationalexpress.com/coach/Airport/London-Stansted-Airport.aspx

But given that the transfer can take nearly two hours, the train all the way there is probably a better bet.

Sunday is of course the day that they tend to rip up parts of the train network, so you need to keep an eye out on whether your journey is likely to be lengthened/delayed at all.