You need a Route: Plus High Speed ticket; your options are:
Anytime Day Return £37.80 Off Peak Return £37.20
Off Peak Day Return £34.80
Obviously only the Off Peak Return is valid to return the next day (this ticket is valid at or after 0930); if you need to travel outside the valid times for this ticket then two singles would be needed.
Really, you should be offered a Route: Not valid on HS1 ticket with an excess for the outbound leg (with the excess priced at half the difference), but by all accounts Southeastern staff are strangely reluctant to do this.
edit: You'd be better off with an Ealing Broadway-Bexhill Off Peak Return, routed +Any Permitted and priced £31.20 (restriction 4B), valid to start short from London. There may be better tickets.
What date and time? --- old post above --- --- new post below ---
OUT:If you wanted to travel early, the 09:42 to Ashford from St Pancras on Platform 11 (HS1) would be ideal which gets there at 10:20 on Platform 6. Then catch the 10:32 (Southern) on Platform 1 to Bexhill, should be there for 11:23.
IN:Again, travelling early catching the 09:39 (Southern) on Platform 2 to St Leonards Warrior Square which gets there on platform 2 at 09:46. Catch the 09:53 (SouthEastern) on Platform 1 to London Charing Cross. OR the 10:04 direct to London Victoria from Bexhill (Southern), this would all be £37.20 off peak return.