@Humbertico, the bus took about an hour and a half, so I would definitely check the price of a taxi. There are probably faster roads, but it's still a bit of a drive. The price would really be the only drawback.
The bus gets you there in time for Vespers at 7pm. I checked into my hotel and then walked over to the church, no problem. It took about 3 minutes. Night Prayer is at 9:30pm.
All services are in chant, 5 from the Office of the Hours, and mass. I will post of photo of the schedule as soon as I take one.
The bus gets back to Burgos around 9:30 am and I headed right out to the Camino. Since my day before was about as relaxing as it gets, I could easily have walked a full day.
If you are in Burgos the morning you head to Santo Domingo, consider going to 9 am mass in the Cathedral. Morning prayer is chanted in Spanish at the start. There must have been 20+ fully-vested clergy in the entrance procession and participating at altar.
The chapel is baroque opulence at its finest and is only accessible during liturgical services. The contrast with the monastery couldn't be more striking. Both beautiful, but both very different.