Bus schedules and tickets

If you don't have a guide book, this page might be helpful: https://www.andalucia.com/travel/bus/home.htm
RometoRio is a helpful website, but always verify the results by going to the web page of the bus company.
Not sure if train is an option on those routes, but Renfe is the train service in Spain.

There is train service to Ronda, but it looks as if the buses take a much more direct, and therefore faster, route. The Damas company operates the buses. You can look up the schedule here: https://damas-sa.es/index.php/rutas-y-horarios/. Your origin will be Sevilla Prado S.S. Click on "Busqueda Avanzada" to select your departure date.

The trip from Ronda to Nerja will be a bit awkward. It involves either train + bus (switching in Malaga) or two buses (again changing in Malaga). The Ronda-Malaga buses are operated by Avanza. The Malaga-Nerga buses are operated by ALSA. I don't know how the train-vs.-bus travel time compares; it may depend on the time of day you want to travel.

It's ALSA again for the Nerja-Seville trip.

You're going to be spending a lot of hours traveling to Nerja for not that much time there. Be sure it's worth it to you, by comparison to spending more time in places like Seville, Cordoba and Granada. I am not a beach person and haven't been to Nerja, but (based on my interests) I'd want a minimum of 3 full days in Seville, 1-1/2 in Cordoba and 1-1/2 in Granada before I'd consider going somewhere else. And I found each of those three cities worth at least one extra day.

I've taken a lot of Spanish buses, and I don't think I've ever bought my tickets more than 24 or 48 hours ahead of time. I can't swear you can wait that long; I know buses do sometimes sell out. However, the only time I was personally affected was when I tried to buy a ticket at a transfer point about 90 minutes before departure and found the bus was already full. I had to wait a couple of hours for the next bus. While I don't think you need to rush to buy the tickets very far in advance, you will be making connections on some of those trips, and there may not be very many departures each day. It could get awkward if one of your preferred buses is full, so I wouldn't recommend waiting until the day of travel in your case.

Long-distance bus tickets in Spain are like train tickets now: You can save some money by buying earlier. You just need to weigh the potential savings against the risk that you'll end up wanting or needing to change your travel plans. ALSA in particular is a very large bus company; I don't think you'll have a problem buying tickets on its website unless there's an issue with your US credit card (always possible). If one of your online purchases doesn't go through, you can probably find a ticket-vending machine (as well as a staffed counter) at the bus station in one of the cities you're visiting earlier in your trip. In my experience if a bus company of some size serves a city, it has a ticket machine there. You'll be able to switch the display language to English if you need to. At least some of the machines allow you to print out a copy of the schedule for your travel day. I find that handy to have.

I believe there's a policy not to sell tickets within X minutes of scheduled departure. I'm not sure whether "X" is 5 or 10, but I think the rule is programmed into the machines as well as observed at staffed counters.

The company Damas runs 7 daily buses from Seville to Ronda. The trip takes between 1:45 and 2:45 hours. A one-way ticket costs 13€. Be aware that in Seville the buses leave from the station Prado de San Sebastian.
To search and book bus tickets, go to www.damas-sa.es. The site is in Spanish not English.
We went to the bus station in person the day before we went to Ronda from Seville and purchased the tickets.