You can take a train from Bexleyheath to Canary Wharf via Lewisham DLR Station in around 34 min. Alternatively, London Buses operates a bus from Bexleyheath to Canary Wharf every 10 minutes. Tickets cost $3 and the journey takes 48 min.
From Barnehurst train to Lewisham DLR Station then train to Canary Wharf DLR Station. 34 min £9. From Bexleyheath Clocktower line 486 bus to North Greenwich Station. 48 min £2. From Bexleyheath taxi to Canary Wharf. 19 min £54. From Bexleyheath drive to Canary Wharf. 19 min £2. From Bexleyheath Uber to Canary Wharf. 19 min £28.