There is no information on how much Radiation is too much for the Bluff Briar. It does get an indicator High Radiation Levels and does not grow. It looks like it might not be able to handle any Radiation. So, maybe it doesn't need an Ambient Radiation information check mark like other plants have?
1) Plant a Bluff Briar.
2) Add a Radiation source until you get High Radiation Levels.