Hi,
It depends on the beardie how comfortable they will be going places. I wouldn't take little ones outside of the home because they are very fast and can easily escape. Bringing them into public places is probably stressful for some of them, but some beardies appear to be chill enough to handle it. I guess it would be trial & error. Definitely do not bring them anywhere where there's food or food preparation because of the salmonella risk.
As for duration, again, it varies. They should get a minimum of 12 hrs of quality light & UV, but natural sunlight is great for them, so it doesn't mean they need to be trapped in their vivs to get it. I usually have my two out for around an hour near bedtime to run around, or more usually, snuggle up & watch tv with me. Others have set up a basking spot in the house & let theirs run around. Some people take them for car rides, too. My opinion (and that's all it is), is that as long as you don't make it a habit having them out from under their lights for long periods of time, doing it once in a while is just fine. I always take a hand towel with me when I take mine outside the house so I can cover them if they get scared and in case they decide to 'let loose' unexpectedly :lol: .