TW9 is basically Kew (are you a Garden botanist?!) and north Richmond.
TW10 (her Profile) is south Richmond, Ham (highly unlikely) and Richmond Park (virtually impossible!).
The “65” bus links Kew Bridge to Richmond and Kingston via Kew Road, passing adjacent to Kew Botanical Gardens.
My guess is that you will be within easy striking distance.
7 Positives and 1 Negative.
Enjoy and Review.