At Heathrow, purchase an Oyster card from machines in the arrivals or information desk. Load it with at least £20 for bus fares; alternatively, use a contactless debit or credit card to tap on buses. Cash is generally not accepted on London buses. The Oyster card allows discounted fares. The single bus fare with an Oyster or contactless is £1.75 per trip.
GBP5 (Oyster card refundable deposit) + fare top-up, 30m
Use your Oyster or contactless card to tap on board bus route 423 from Heathrow. The fare is £1.75. The bus journey takes roughly 50 minutes to Paddington area where your hotel is located.
Bus to Arsenal Stadium from Stamford Bridge area. You may need to transfer at a major stop (bus fares remain £1.75 per trip). Tour at 11am approx. £25, prebooking advised.
GBP3.5 (two bus fares) + GBP25, 1h travel + 2h tour
From Piccadilly, take bus 15 or 9 towards Tate Modern via South Bank. Fare £1.75. The museum opens 10am, so consider walking along the Thames beforehand.
Take bus 423 or alternative airport coach from central London (Victoria Coach Station or Paddington) to Heathrow; fare about £6-10 - confirm route and tap Oyster or use prepaid coach ticket. This trip can take 1h-1h30m. Budget 3 hours total for travel and airport procedures.