Oh... You said "if possible". They're still bleeding out and from what I understand taking 10 would take 10 rounds worth of time. So... Yeah. I just figured I'd stick with the "if possible" to give them a chance.
Granted I might be misinterpreting what Taking 10 does.
Yeah, no, not how Taking 10 works. For comparison:
Taking 20 is basically "Well, if I roll the dice enough times I'll
eventually hit 20, and if there's no penalty for failure, there's nothing to stop me doing that. Call it 20 rolls on average, so 20 attempts, so basically you take twenty times as long and automatically roll 20." For Single Standard Action rolls, this takes 2 minutes. This is mostly a time-saving measure, since sitting around while someone makes 20 rolls every time they come to a lock they can't open or the like would get really old really fast.
Taking 10 is more of a "I am going to do this task to standard performance levels, so I don't risk rolling low but I don't have the possibility of rolling high." It's basically a representation of a skill that you have sufficient training at that you won't likely be botching it every few times you do it, which the randomness of the dice would otherwise cause. It does not take any longer, though it does require your concentration on the task at hand.
You can use it where there are risks to failure, though if you don't know the DC of whatever you're doing, doing so may not be a good idea.
Also note that if you don't have sufficient ranks+modifiers in the skill to represent that "sufficient training," ie DC-10, you have 0 chance of success, and will have to roll it, assuming Taking 10 didn't screw things up for you; If Freda had Taken 10, for instance, she'd have auto-failed, and that would have taken a round, and thus potentially another point of HP.
Also also, "Distractions or threats (such as combat) make it impossible for a character to take 10." Exactly what constitutes a "distraction or threat" is somewhat up to the DM, though do note that any skill except UMD can theoretically let you Take 10, so something like "in conversation" or "high up" probably shouldn't count.