De Beurs is very nice place and in my opinion it is the best place near Schiphol.
The train from Hoofddorp (Beneden station) to the airports takes around 4 minutes.
You can get from the hotel to the train station by bus (140 is very close, 168/169 also an option). However the hotel is at walking distance (around 2 km) so you might go on foot.
I've just checked the train schedule (ns.nl) and the first train for the day is at 5:20 AM (5:24 AM at Schiphol). If you can afford being there half an hour past 5 am it is a good option. The train ticket costs 2.10 EUR (make sure you have coins as there is no desk and you have to use the ticket machine).
I've checked the the bus schedule (9292.nl) and the first bus(169) arrives at 5:30. Unfortunately you will have to walk to the train station unless you are OK with the next train at 5:36 (5:40 at Schiphol).
I think there is not other way with public transportation. Probably a taxi but I'm not familiar and you should ask at the hotel. I know there is a hotel shuttle service for Amsterdam but I don't know if it covers Hoofddorp too. However I expect these options to be highly costly.
My flight was later in the day so the train was just fine for me.
I hope I have helped.
Best regards and have a pleasant travel