David, we just started our latest mini-Camino at the Logroño bus station a couple of weeks back.
The short answer is, just go out the front door of the bus station, start walking west and ask someone. That's what we did.
The long answer probably won't make sense without looking at Google Maps...
Our westward route took us down Avenida Pérez Galdos. When Pérez Galdos teed into another street, a local saw us looking confused and pointed us to the Camino. We saw the arrows within a block or so after that.
However, if Calle Duques de Nájera is a landmark for you, it looks like you can take a hard left out of the front door of the bus station and walk south on Calle General Vara de Rey, then in three long blocks you'll hit Duques de Nájera and take a right.
I'd recommend looking at the map anyway:
https://www.google.com/maps/place/Estación+de+Autobuses+de+Logroño/@42.4594655,-2.4622842,15z/data=!4m5!3m4!1s0x0:0x32dc90266b37d419!8m2!3d42.4599404!4d-2.4442168
The walk out of Logroño is lovely. Enjoy!