The Proposal co-stars were snapped by TMZ photographers as they scaled mountains at Grand Teton National Park in Wyoming with a group of friends.
Reynolds was also spotted spending time at the Bullock family home in Jackson Hole in recent days.
Bullock surprised Reynolds at the LA premiere of his latest movie The Change-Up a few weeks ago and posed for a series of pictures with the actor on the red carpet.
The stars were romantically linked earlier this year when they spent New Year's Eve together in Austin, TX.
Bullock later dismissed any suggestion that she and Reynolds were dating by teasing: "I think there will be a collective sigh amongst woman across the United States when I say he is not my lover."
Reynolds's latest movie The Change-Up is now playing the US and opens on September 16 in the UK.
> Sandra Bullock was keen to get back to work, says director
> Ryan Reynolds unsure about Green Lantern 2
Watch a trailer for The Change-Up below (mature content):