How far do I “pull over” in a bike lane? If I am riding down a marked bike lane on a road which is adjacent to the curb, and I need to stop for a very short time (e.g. to adjust something, turn on lights, or drink some water), how far should I get off the road?

That is: As a car driver, if I had to stop I would move onto the shoulder of the road, or otherwise as far right (US, drive on the right) as is safe for the vehicle. With a bicycle lane, there is no specific shoulder, but I can pick up the bike and move off the road entirely. Should I take the time to do so, even if there is essentially no traffic?

What if the lane is especially wide (e.g. if it is a bicycle lane to the left of parking space, but with no cars actually present), or if it is only a generously wide road without any markings?

(I am looking for a safety and politeness perspective, not regional traffic laws, though if there is a general trend in law on the matter that is also useful information.)
Please don't block the bike lane or traffic or parking spaces, but use your best judgement; in that order.

Personally I feel a curb is a logical and physical barrier which protects you from the activities of the traffic way. 

Protection
Getting on a curb means a car that hits you has already been slowed down by a 6 in. cement block applied up to 4 times (4 tires) against the cars momentum. Ever see a car hit a curb? Sure they can plow over it, but they definitely slow down, and change direction. When riding you have several options to evade, but when on foot you are much slower/less agile. Use the curb as a natural defense. Also, I'm not a law expert but I'm sure there are better legal protections for being off the road with regards to this matter.

Courtesy
Do you look everywhere and try to decide what everyone will do before they do it while riding. I sure hope you do, it will help keep you safe if you can anticipate situations, both while riding and while driving. If you remove yourself from the bike lane you become a non-player to those using the traffic ways. The cars don't have to decide if you might fall over while mounting/dismounting/precariously balancing while tying shoes etc. Like wise for bikers, will you see them when you decide to start? How straight will your line be when you do start etc. Even if you pull over far and look before you start up, you have forced others to do the extra work of thinking through possible scenarios and possibly slowing down, changing lanes or changing routes around a block where you are 'pulled over'. 

If you are on a long straight away with no intersections and you can anticipate the traffic for the next 2 min, and you will only take 20secs then who cares. If you don't see anyone, but a car could pull up from around the block in less than 10 secs even though it seems dead you should probably just get over the curb.