Take the new SGR Madaraka Train , journey takes 5 hours. Departs twice daily.
Other option is domestic flight with Fly540, JamboJet, AirKenya, Skyward Express.
Road trip takes 8-10 hours, sometimes even longer if there's construction & diversions.
The only beauty you can enjoy on that road trip is white knuckles, from holding the seat in front of you, due to the reckless drivers. Also you get to see the back of many slow moving trucks, which at times are hard to overtake.
If you do take the trip, stop at the Sikh Temple in Makindu. It's an institution among the Kenyan Sikh, and Indian community.
Very comfortable, fully air conditioned and drivers changed half way through the journey and they drove carefully, not to be compared with those mad matatu drivers.
ALWAYS take the daytime departures, never the night.
Plenty of wildlife to spot en route.
We recently visited Makindu Gurdwara from Mombasa. The Road from Mombasa is being reconstructed and we experienced very heavy traffic leaving Mombasa. Took us 6.5 hours to do the 200 miles. (We hired a driver and MPV). I would suggest taking the train.They're comfortable and reasonable.
Just finished the Mombasa road journey yesterday. Road warrior Africa is correct: white knuckles for the entire 400 km from Amboselli junction to Mombasa. Nothing enjoyable about thousands of large trucks driving like crazy with no regard to safety. No animals other than some sorry red zebras (due to all the dust) and a few baboons.
If you can get a ticket, take the train.