Investigators said the abuse began Thursday evening and lasted through much of the night.
The victim surreptitiously slipped the note to one of her two elementary school children, with instructions to pass it on to the bus driver, Trujillo said.
Alvarado is accused of threatening to kill the woman and trying to suffocate her with a pillow and then a shirt. Investigators also allege that he took her cellphone to prevent her from calling for help, Trujillo said.
The abuse may have occurred in the presence of two schoolchildren as well as a toddler, Trujillo said.
Van Wamel, the contract manager for the STS bus service for the Las Cruces Public Schools, said the driver who alerted police worked for the company for about four years. The two children, he said, are students at Jornada Elementary School.