I see ALSA and RENFE and both get in late.
Are there any other options?
In addition to the train option I quote below,
www.autocaresrabel.com has an early morning bus from Burgos to Palencia from Mondays to Fridays (except public holidays). They say in their web that they make the route from Palencia to León too but they don't offer schedules for that one... so you will need to get in touch with them to confirm if they really make it and to ask for schedules. If you get in touch with them, you might ask also for the arrival time of the bus(es) from Burgos because their schedules just quote the departure time from your departure point but not the arrival time to your destination. Once in Palencia, if there isn't a bus to León that suits you, you can take a train to reach León... depending on the arrival time of the bus from Burgos, you might be able to get an earlier train to León than the one you would take if you had taken a train from Burgos to Palencia but to know it for sure, you would need to confirm with Autocares Rabel the arrival time of the bus from Burgos. If it doesn't arrive early enough as to take an earlier train, I wouldn't bother and I would make all the route by train changing trains in Palencia.
Notes: if you had to take a high-speed train from Palencia to León, book it in advance to (try to) get it cheaper. If you see two trains departing and arriving at the same time, that means they are a single train; a high-speed train that is also sold as a MD/Intercity/Regional train but the number of seats sold with MD/Intercity/Regional fare is limited so booking well in advance is a good idea to avoid having to pay full high speed train fare (or even to avoid finding the train full on your travel date).
It actually works out better to take Renfe to Valladolid and Valladolid to Leon.
It might even work doing the transfer at Venta de Banos.
...and, even better, changing trains in Palencia. Unless Anniesantiago is traveling on a Sunday, that option (to change trains in Palencia) will allow her to arrive to León before 14:00.