During short visit to London.
Is it possible to go from Gatwick airport to central London (Chiswell street ) by bus on Sunday morning at 10am?
So, yes, although I recommend the trains, they're far more convenient.
However, if you do want a bus, you could either take a coach into Victoria Station with National Express or EasyJet's buses.
The trains are a LOT faster as well.
By bus, it'll take about 3 hours.
10 mins walking - Walk to Gatwick Airport, A23 South Terminal
23 mins bus - 420 bus to Redhill Bus Station
41 mins bus - 405 bus to Whitgift Centre
1 hr 0 min bus - 468 bus to Elephant & Castle Station
18 mins bus - 35 bus to Liverpool Street Station
15 mins walking - Walk to 34 Chiswell Street, City
Arrival time: 13:10
If you're prepared to take other forms of transport, it's only about 1 hour and 15 minutes
Using the TFL route planner on http://tfl.gov.uk going from Gatwick Airport to Barbican (which is the nearest underground station) and only allowing buses and coaches and leaving on Sunday the 18th at 10am it suggests:
5 mins : Walk to Gatwick Airport, South Terminal Bus Station #nrc
1 hr 10 mins: Express bus ESB3 to Waterloo Station / York Road
11 mins : RV1 bus to Waterloo Bridge / South Bank
15 mins: 4 bus to Barbican station
Arrive: 12.06 - journey time: 2hr 1min
If you were to ignore coaches (which are really just a type of bus), you are given:
10 mins: Walk to Gatwick Airport, A23 South Terminal
23 mins: 420 bus to Redhill Bus Station
41 mins: 405 bus to Whitgift Centre
1hr 0 mins: 468 bus to Elephant and Castle Station
5 mins: Walk to Elephant and Castle / London Road
18 mins: 63 bus or 45 bus to Snow Hill (EC1)
10 mins: Walk to Barbican (London), Barbican
Arrive: 13:06 - journey time 3hrs 4 mins
Allowing all transport modes gives the following quick route:
49 mins: Southern train to London Victoria Rail Station
3mins: Underground Victoria Line to Oxford Circus Underground Station
5mins: Underground Central line to St Paul's Underground Station
9mins: Walk to King Edward Street (EC1)
11mins: 56 bus to Barbican Station