The cheapest way there is by bus. You can buy a ticket at Novello's bus station in BC and tranfer in Belmopan and from there to Griga. Total one way fare maybe $ 5-6USD.
If you take a taxi it will definitely cost more. Fuel cost are very high right now, even more than the US. Now, you can always haggle with some drivers, but it might cost you $75.00USD or more for the drive one way. They gotta make a living, too.
Taxis around BC are fine, but on the bus you travel with the locals, see the country side and it's cheap. Can't beat that! A lot of Novello buses are refurbished Blue Birds from the US. Do you remember riding those in middle school? If you're my age you might! Haha.
Dangriga is a beautiful village with lovely people. Have some hudutz while you're there - awesome Garifuna dish of mash plantain and fish. And try some cassava bread with a bit of dried mackarel. Hella good!
The best deal for breakfast there is at King Burger. Oh, and definitely listen to the student singers in the parade singing traditional songs. Something splendid to behold. Bring a camera!