Yes? Ask your GM for confirmation, though.
The answer to your question depends on how you interpret the life bubble spell's description, and more specifically, on how you interpret its first sentence. That sentence is as follows:
You surround the touched creatures with a constant and moveable 1-inch shell of tolerable living conditions.
There are three ways in which you could potentially interpret this:
- The first sentence of the spell, and the various specific immunities that the spell grants, are independent effects that don't interact and should be adjudicated separately.
- The first sentence of the spell is just flavour text. The spell's actual effect is everything that follows it.
- The first sentence of the spell description is the effect of the spell, and everything that follows that first sentence are examples of that effect intended to clarify how it works.
The first interpretation is implausible, because spells do not usually work that way: Usually, spell descriptions in the core rules and advanced player's guide (from whence life bubble comes) have a well-defined in-universe effect whose mechanical effects are laid out in the spell description; spells that provide a laundry list of unconnected effects are rare. More importantly, if the first interpretation was correct, and the first sentence was supposed to be separate to the other listed effects of the spell, that first effect would have no clearly-defined mechanics to apply, and thus would be almost impossible to adjudicate.
The second interpretation is also implausible, because spells in the core rules and advanced player's guide do not usually open with a line of meaningless fluff text that is utterly divorced from the rules: Every sentence in a spell's description is part of the description of that spell's effects.
That leaves us with the third interpretation as the only possible valid one: The first sentence of the spell describes the spell's effect, and everything that follows is just examples intended to clarify how it works in play.
So, life bubble surrounds the touched creatures with a constant and moveable 1-inch shell of tolerable living conditions. Everything after that is just an example of the kind of protections that one-inch shell offers - and crucially, there is every reason to believe it is a non-exclusive list.
Take this line, for example:
Life bubble does not provide protection from negative or positive energy (such as found on the Negative and Positive Energy planes)
If the list of immunities provided by life bubble is supposed to be an exclusive list, there would be no need to mention positive and negative energy as things it doesn't protect against, as they are not exceptions to any of the immunities explicitly listed in life bubble's description. We can therefore safely assume that life bubble's "1-inch shell of tolerable living conditions" is supposed to protect against environmental conditions not explicitly included in the listed examples of what the spell protects against.
With that dealt with, we have to ask: Is radiation included in the list of environmental conditions that life bubble protects against?
This is where a hint of uncertainty creeps into my answer. Life bubble's spell description isn't explicit about whether Life Bubble protects against radiation, most likely because radiation wasn't something the spell's authors considered when they wrote it. Still, the rules for radiation that you linked do make it seem like a harmful environmental condition of the sort the spell is designed to protect adventurers against, so it seems reasonable to rule that it's an effective form of protection - and radiation is a less severe environmental condition than being submerged in acid (which life bubble definitely does protect against), so I believe that life bubble is an effective protection against radiation.