travel between Spain & Portugal

The roads don't go straight from Seville to Lisbon due to Western Spain's geography.

You'd do best to check into TAP Portugal airline to see what the airfares are. I'd suggest flying and they're the only airline going between those points.

Per David, TAP has direct flights between the two cities. Takes about an hour, and the cost is less than US $60.

Since the Algarve is not on the RS Portugal tour itinerary, I'd recommend spending your three nights somewhere along the Algarve coast, like Lagos. Last May, my wife and I took a bus from Seville to Faro Airport, where we picked up a rental car for our two weeks in Portugal. The bus was fast, comfortable and cheap- about 2:15 hours, for around 15 euros. The same bus goes as far as Lagos, at about four hours, with stops at Albufeira an Portimao along the way. You can train from (at least) Lagos or Faro to Lisbon on the day you meet up with the tour group. If you're not driving, I'd suggest Lagos as a good base for three nights as it offers enough to see and do for a couple of days.

We took the Spain tour this past summer. We are doing the Portugal tour next summer as well. We stayed on in Sevilla for a few days. We really enjoyed that place and a day trip to see the Mezquita in Cordoba was more than worth it. We are getting to Lisbon a day early to see Sintra, so that is an option to consider as well. But hard for me to envision it would be as much fun as Sevilla. Enjoy!

Check Kayak-this September we flew Seville-Madrid-Lisbon on Iberia for €125 a person. Can't help with what to do in the interim as not familiar with where the tours go. If south, take a train north to Porto from Lisbon, or if it goes north, rent a car and check out the algave. We absolutely fell in love with Porto and the Douro region.

Thank you all for your prompt replies. We think we will take the bus to Lagos, and stay a couple of nights, maybe with a day trip to Salema by bus, then take the train north to Lisbon the day before our tour starts. We appreciate all of the good information!

Salema is where we stayed for our four nights on the Algarve coast. We loved it as a base for exploring the area by car, and to come back to at night. But I would definitely not recommend it as a place to visit by bus from Lagos, especially if you only have one full day in Lagos. Salema is small. It has a few restaurants and a nice beach, but nothing to see. Lagos has lots of restaurants, lots of nicer beaches, and a few sights to visit. Take the day off, and enjoy Lagos- walk along the cliffs, or rent a kayak and see them from the water. If you really want to bus somewhere, Sagres is only 15 km past Salema.

It looks like the bus from Sevilla takes nearly 5.5 hours and the train to Lisbon 4 hours train time plus whatever the connection time is. So with 3 days, you'll use half (or more) of 2 just changing locations (take into account time to pack/unpack, get to/from stations). That gives you one full day and a few hours in Lagos.

The RS tour doesn't include Cordoba - an easy day trip from Sevilla. There's lots too see there, including the Mezquita, easily the best attraction in Spain after the Alhambra, and unique.

The 9:00 am bus from Seville arrives in Lagos at noon. That's four hours, with a one hour time zone change. That gives you a good day and a half in Lagos, if you're staying two nights. The train from Lagos to Lisbon Oriente takes about four hours, with a connection in Tunes. From Oriente, you can take the metro into central Lisbon in 25-30 minutes. A more efficient option is to take a bus directly from Lagos to central Lisbon (eva-bus.com), in 3:45 hours. Any public transit land option from Seville to Lisbon takes around eight hours, and probably involves a bus for at least part of the route. So unless you want to fly from Seville to Lisbon, a two night stay in Lagos will cost at most two hours of extra travel.
Edit: Note that there are two different bus lines involved here. From Seville to Lagos, use Alsa, the Spanish line. Eva is the Portuguese line, for the trip from Lagos to Lisbon.

We found the bus more convenient from Lagos to Lisbon - which disappointed this train lover - but we were in a condo 2 blocks from the bus station

We did take the Alfa from Lisbon to Porto. I enjoyed that lot