The appropriate/best/cheapest ticket to Stansted when holding an existing Travelcard is not entirely straightforward.
Firstly the stations 'Stansted Airport' and 'Stansted Mountfichet' are grouped, which means you can double back between them as part of a journey to a station associated with 'Stansted Group', which stations just beyond Stansted will be when travelling from London.
In particular, the following journey is permitted on a London-Elsenham (Essex) ticket:
London-Stansted Airport
Stansted Airport-Stansted Mountfichet
Stansted Mountfichet-Elsenham (Essex)
because there is no doubling back, except within the station group Stansted, which is allowed.
So that ticket is valid on the direct Stansted Express to stop short at Stansted Airport, as most notably is Audley End, which has XC service direct from Stansted Airport
You hold a travelcard so typically you'd buy a ticket from the edge of the boundaries, however there is additional complication here, which is that the edge of the boundary on this journey is at Enfield Lock (or beyond it), which is associated with Stansted Group, so from Enfield Lock to Stansted you are not a permitted route to Elsenham since the only permitted route is the direct or shortest route (or 3 miles beyond it), since there clearly could be no mapped route from Stansted Group (Enfield Lock) to Stansted Group (Elsenham (Essex))
However according to the following discussion
http://www.railforums.co.uk/showthread.php?t=68320
you don't consider Enfield Lock, but rather you consider the two tickets together, so the BZ ticket is valid since the origin, Tottenham Hale (you could travel from Liverpool Street if more convenient), is in a different routeing group, and in fact you can probably consider routes from LST to SSD even starting at TOM with a BZ6 ticket.
So you buy BZ6-Elsenham (Essex) at TOM or LST station and just use the Stansted Express direct to Stansted Airport. No change required.
Cost £10 for an anytime single
If you didn't want to queue up and buy your slightly dubious ticket, you could just buy TOM-Elsenham online, but this costs £12.20 for a super-offpeak single. Valid from LST and TOM also.
Total cost is £20 with the BZ6 ticket, or £13.20 with a Network Railcard or similar.