Uvalde Police Lieutenant Daniel Rodriguez said one man called the dispatch line to report that a white pickup truck was swerving on the road.
"[The caller] was scared [the pick-up driver] was going to cause an accident and asked us to send deputies," Mr Rodriguez said.
"Deputies were dispatched, but before they could reach the area, the same caller called 911 to report that the truck had been in an accident."
Dispatchers in Real County also received a call from a woman who reported a truck was driving erratically on highway US 83, county Constable Nathan Johnson said.
The Texas Department of Public Safety refused to speculate about what caused the head-on collision near the town of Concan, although one spokesman said the truck driver appeared to have crossed the centre line.
Twelve passengers on board and driver Murray William Barrett, 67, died at the scene, DPS Lieutenant Johnny Hernandez said. Another bus passenger died later at a San Antonio hospital.
The pick-up truck driver, Jack Dillon Young, 20, of Leakey, Texas, was in a stable condition and the lone survivor from the bus remained in hospital in critical condition late on Wednesday.
Family members of the victims react to the news outside First Baptist Church in New Braunfels
Brad McLean, senior pastor of First Baptist Church of New Braunfels, Texas, said: "These are individuals we've sat next to and had dinner with and laughed with and cried with and worshipped with. They were part of our church family.
"I think it's the everyday interaction and relationship that has been built that, boy, those are the things that really will affect us a week from now, a month from now, a year from now."
All of those who died in the tragedy were between 61 and 87 years old.
According to CBS, church members are struggling to come to terms with what has happened.
Property manager Jamie Anderson of National Church Residences told CBS: "We're talking 30-40 years in relationships. That would be devastational to anyone, so can you imagine losing your best friend?"
The church has set up a counselling service to help the bereaved.
In a Facebook statement, the church thanked people for the "compassionate outpouring of support and prayers" and have set up a fundraising page to support victims' family members.