By train, it takes between 55 minutes and 1 hr 15 each way, with one change at either Barnham or Three Bridges (occasionally two changes at Hove and Three Bridges)
Train would not be cheap.
Yeah, according to National Rail (
http://ojp.nationalrail.co.uk/en/s/seasonticket/calculator), an annual train ticket between Brighton and Horsham (on any route option between the two) will cost £2,456. There's another annual ticket option for £1,988 but it is only valid on journeys that travel through or change at Haywards Heath.
Alternatively, a daily ticket will cost about £18 round trip (so a daily ticket 5 days a week for a year would be almost £5,000).
and by bus (Compass buses) about 1 hr 15 minutes.
Doing a quick search online, it seems that Compass buses only run the service between Brighton and Horsham (number 17 bus) on Sundays and Bank Holidays - during the week, the number 17 bus is run by Stagecoach. Looking on the Stagecoach website, the bus seems to take about 1.5 hours and an annual megarider ticket in the South costs £740 (
http://www.stagecoachbus.com/timetables.aspx?serviceid=30&locationId=26&from=&to=&locval=108).
Alternatively, if you were to drive between Brighton and Horsham, it would take about 40 minutes (it's 23 miles) and would probably cost between about £5 and £10 a day for gas, depending on how fuel efficient the car is (so between about £1300 and £2600 for a year, travelling 5 days per week).