The third-year kicker will be challenged by undrafted rookie Chris Boswell from Rice.
While the Texans haven't released their entire list of undrafted rookies, at Monday's Houston Texans Charity Golf Classic, general manager Rick Smith was asked specifically about the signing of Boswell.
"He’s got a big leg," Smith said. "He came and he did a really good job at our pro day. We had our local workout. He was a very impressive man in that environment."
Connecting on 65 of his career 88 attempts (73.9%), Boswell drilled three field goals from 55 yards or longer. His career-long was a 57-yarder against Louisiana Tech in 2012. Boswell also converted a unique onside-kick at Reliant Stadium in a contest against Houston.
Bullock was 26-for-35 (74.3%) in 2013 with the Texans, nailing a 41-yarder in Week 1 to give the
"I think he actually is working out with Randy a little bit, so he knows his competition," Smith said. "They know each other, and it will be fun to watch."
As far as head coach Bill O'Brien is concerned, the kicker position is like any other on the team, in terms of competition.
"The whole goal in the draft process and free agency is to try to create the most competitive roster you can create," O'Brien said. "Where guys go out there every day, and they know that they have to go out and compete and perform and play to the best of their ability. So at any point, at any position, whoever we brought in, that’s the mindset."
Boswell, the rest of the undrafted rookies, as well as the 2014 Texans draft class, will take part in a rookie mini-camp from Friday through Sunday.