How would you get to Portugal from Rota, Spain without a car. Using a bus to a train station. Anyone know? I imagine you might need to get to Sevilla?
Rome2Rio.com is a good first step in answering questions like this. I used Faro as a destination since you didn't specify a city. The suggested bus and car routes were both through Seville. It appears that your first opportunity to hop on a train might be in Tavira or Villa Real de Santo Antonio (on the Algarve), but I don't know how they would work with a bus connection; Faro might be better.
It's possible that your trip would be faster if done only on buses.
Yeah, you pretty much have to go through Sevilla. There is a bus from Sevilla to Faro or you can take a bus straight into Lagos (5.5hrs). Not sure where you are off to, but there is also a bus from Sevilla to Lisbon.