I don't know that a taxi would be faster. I would probably arrange a private transfer with a company such as www.romeshuttlelimousine.com.
Looks like you can take the metro from Termini. €5 for the bus from the airport plus €1.5 for the metro.
Up to you to decide if the €30 for the taxi is worth it.Edited: 20 September 2018, 15:30
What bus station?