Is this terminal easy to navigate? Yes;
as long as your taxi brings you into Busta Shinjuku,
it's easy to get to your bus stop, I think.
https://shinjuku-busterminal.co.jp/en/floormap/3f.htmlOn the 3rd floor,
your taxi passes by the bus arrival area and the taxi pick-up area
before reaching the taxi drop-off stand.
Getting off your taxi, you soon find the nearby elevator.
The up escalator is a bit away, over the down escalator.
The bus departure stand is on the 4th floor.
The name "Shinjuku Expressway Bus Terminal"
has been used since before the bus terminal was moved there.
We will take a taxi to the bus station though.You will get to Busta Shinjuku in around 10 minutes,
and pay about 1000 to 1500 yen per car.
If your taxi runs very slowly, the fare may pile up, as time goes by.
Also, Tokyo taxi fares are set higher during late and early hours,
from 10 p.m. to 5 a.m., by 20 percent.
It seems taxis from your hotel have to make a detour,
because there is a
red zone (where drivers cannot park or pause)
in front of JR Shinjuku Station South Exit,
on Kōshū Kaidō.
While your taxi runs eastbound there on Kōshū Kaidō,
you may see
JR Shinjuku Station to your left (the north)
and Busta Shinjuku to your right (the south),
but you still have several minutes.
I suggest you write down on paper or type on your smartphone
like "Busta Shinjuku (3F) Taxi Drop-off"
and show it to your taxi driver at the beginning,
so that you are never dropped off in the red zone.
Enjoy your trips!