Transport from Granada to Toledo

Well.....this isn't exactly great news......using the site listed below, I found that there is an AVE (high speed train) leaving Granada at 3:35 p.m. (15:35) on October 1st arriving in Toledo at 8:23 p.m. (20:23) with two connections for 125 Euros (second class ticket). There are a number of "slow trains" making the journey with twice the travel time at less than 1/3 the cost.
Here's a good resource for train travel: https://www.seat61.com/Spain-trains.htm#Spanish_train_classes
I have no experience with Spanish bus service.

Judith,

You can travel by train, or bus, from Granada to Madrid ( Puerta de Atocha Train Station)
Once you arrive to Madrid, you’ll need to transfer to the AVANT train to Toledo (30 minute journey)

You can check train schedules here

BTW, did you book your Alhambra Tickets yet? If not, do so ASAP!

Enjoy your trip!

Edited to add...
If time permits, you may consider spending an overnight in Córdoba en-route to Madrid.

It may be too late to change your itinerary, so the following information is only for the sake of helping others who may be planning a trip to Andalucía.

On our last trip to Spain, my mom and I traveled this route:
Flew into Madrid > took train to Córdoba upon our arrival > Granada > Sevilla > Toledo (vía Madrid)
(We’d visited Madrid on a previous visit so we skipped it this time)

The main reason for taking this route was to avoid the long trek from Granada to Madrid, albeit this was before the direct AVE train became available (on this route)

According to Renfe, there are only 3 trains/ day traveling from Granada to Madrid.
You may consider taking the direct ALSA Bus , although it will be a longer journey than the train.

Book separate tickets. Granada to Atocha, then Atocha to Toledo. These latter tickets don't offer much savings booking ahead. You won't need a lot of time between trains, but if you have to go through security, it will be like the airport, so I would aim for 30 minutes.

Direct trains from Granada to Madrid depart around 7:00, 15:00, and 19:00, the last being too late to connect by train to Toledo. Schedules are currently only published through Oct. 14. Wait at least two weeks to check later dates.

Thanks everyone. It is frustrating that the schedules aren’t available further in advance! The websites and recommendations are useful. I didn’t realize that we’d have to go to Madrid to get to Toledo! We do have Alhambra tickets, but I guess I should get the Seville Alcazar tickets ahead of time also.

Yes, don't plan to walk up to the Alcazar and buy tickets on the spot unless you like. lines. A lot.

The renfe.com website doesn't do well with connections. Toledo is on a spur rail line connected only to Madrid, so you should make two separate purchases.

You could drive it in about 5 hours, and stop at Campo de Criptana or Consuegra en route to see the windmills and castle. Fewer hours if you didn’t stop to sightsee.