Hi, I live in Burgess Hill myself and commute to London Bridge daily.
Depending on where you actually live in Burgess Hill, and how far you are prepared to walk means that you could have the choice of Two stations (Burgess Hill and Wivelsfield).
I live closer to Wivelsfield so in the mornings I catch the 07:08 to London Bridge which comes up from Eastbourne and there is never too much trouble getting a seat (unless the train is short formed for example).
Trains which come up from the Coastway West (Littlehampton/Worthing, etc) after often busier and you do run the risk of possibly having to stand. The same could be said of Brighton services.
The biggest problem with Wivelsfield is getting home in the Evening Peak. There are only two direct trains from LBG (17:23 and 18:23). Even changing at Haywards Heath can leave you with a 15minute wait for a connecting service.
There is a better service to Burgess Hill with the 16:57, 17:42, 17:57, 18:12 and 18:27 all running direct. Also, should you catch an Eastbourne Train you can pick up a Burgess Hill train quite easily from Haywards Heath as some of the Victoria 'Gatiwick Express' services stop there.
For some reason there are three 'Gatwick Express' services that stop at Wivelsfield in the Morning Peak, but NONE at all in the Evening Peak, which I always think makes the Service at Wivelsfield a bit lop-sided. It is as though Southern are saying "We'll get you to Work, just don't expect us to get you home again!"
I did question this with Southern a few years ago and was told that Wivelsfield was now classed as "Coastway East" station - which I didn't fully understand as it is clearly on the BML!!
Off peak, the London Bridge - Wivelsfield/Burgess Hill Service is every 30mins provided by FCC.
I hope that helps - plus there are TONS of new houses being built in Burgess Hill at the moment, so you shouldn't have much trouble finding somewhere to live!
