You can get a taxi from Negombo to Kandy less hassle than using public transport, for me I prefer public transport as you experience more.
First make you way to Colombo bus station, via taxi, or local bus.
From Colombo Central Bus Stand – Fort - Peliyagoda - Nelundeniya - Kegalle - Kandy
Buses to Kandy run 24 hours per day from the Central Bus Stand in Colombo Fort area, leaving every 15 minutes between 4am and midnight, with a slightly reduced service through the night.
Online booking: https://busseat.lk or https://www.busbooking.lk
First catch the train from Negombo station to Colombo Fort Railway Station trains start service 06:27 ends 20:41.
Inter-city (ICE) and Express Trains between Colombo-Kandy and run from 05:55 ends at 17:45.
Check times click here