£1.50 for a bus trip
The cheaper Paper travel card you can get is zones 1-4 which is £12.70 (for reference the Oyster cap for this is £9.80 so significantly less and that's true of all paper tickets in London) while if your wife is only interested in the centre of London then the Oyster zone 1-2 Daily cap is £6.80 - factor in the £3 Oyster deposit which is refundable as is any unused credit then that would save you a fair bit of money if you're willing to deal with a little hassle in getting that refund.