There's a handy-dandy link in the Persuasion FAQ to a Persuasion timeline worked out by an Austen scholar (and linked below). Ms. Moody puts Wentworth's arrival at Kellynch about Oct. 8. The Long Walk takes place "one fine November day," and the trip to Lyme "a day in the middle of November." Since he was gone a couple of days and then there was a couple more to make arrangements before the trip, I'd say that four weeks, five tops, between Wentworth's arrival and the Long Walk seems right to me.