ALSA

The biggest company for buses in Spain is Alsa.
You can find bus information and book online to and from almost everywhere in Spain.

Many buses have wifi, toilets etc.
You can book online and show the screen of you smartphone as if it were a ticket.

Just go to
https://alsa.com

It is possible to transport pets on buses in Spain.
See more info here
https://www.alsa.com/en/web/bus/alsa-experience/plan-your-journey/pet-transportation

Alsa have some very interesting bus pass offers.
For example you can buy a pass to go anywhere in Andalucia for 7 days for a fixed price.

https://www.alsa.com/en/web/bus/offers-and-passes/passes/buy-your-pass

Eurolines:
If you want to make a big international bus journey it is a good idea to check if eurolines have any good prices. They have routes all over Europe. They used to have good rates between Granada and Lisbon.

https://www.eurolines.eu