I've had to commute routes where I need to use a narrow staircase to go up and down a pedestrian bridge over a highway.

For starters, any place where you have to share narrow space with pedestrian, the polite way to do so is to dismount.

I shoulder the bike or walk it. The bike always goes to the far side ( If there is a fence or wall, the bike goes towards that fence or wall or guard rail. ) so there is less chance to hit another person with a protruding pedal or handlebar.

While going down stairs, I sometimes roll the bike on its rear wheel, holding the handlebar up and using the brake to control it. That way my combined bike+rider width is minimal and that will let another pedestrian pass, even if they are also carrying a bulky load.

Consider that even if you believe to have good control over the bike, there might be something out of your sight that may cause you to temporarily lose control or may need you to perform an unexpected maneuver (e.g. a piece of garbage you ride over and it makes you lose traction). If that happens at the wrong time, you may hit another staircase user. Better to play it safe and dismount.

I've ridden in a city where there are shared bridges (pedestrian/alternative transport) but it is mandatory to get off your bike, skateboard, or whatever you are riding. You mount again on the other side where there is a wider and dedicated cycle path and a walking lane.

Frankly if you're going up/down steps, you're in the pedestrian's space and not somewhere suitable for cycling.

You know how sometimes vehicle traffic intrudes on our cycle lanes? Parking inconsiderately, putting cyclists at risk?
That's what you'd be doing to the pedestrians by riding in their space. Don't be that-guy.

Your solutions are to either walk the bike (to become a pedestrian with a load, travelling at walking speed) or to find a cycle-safe route that gets you to your destination.

I would not ride in pedestrian areas - that may not even be legal depending on where in the world it is.

Yes, you can prevent this situation. Don't go down the stairs on your bicycle (and most likely not even carrying it, if it is so narrow).

It's not possible that there are only two ways to get to your destination, unless you live on the very top of a hill. You are presenting us two options:

• boring way (path A);
• short, fun, most likely with an illegal stretch (path B);

I guess you are simply comparing the two shortest path, one fully legal and one which is short and allowing access to some fun section after (or just before) the stairs you mention. Think out of the box: let's assume path A is boring and it takes 25 minutes to complete it, while path B is fun and it takes 35 minutes to complete (walking the bicycle down the stairs, 33 minutes if you pedal down the stairs). I cannot believe that you cannot find a path C that would take you to the destination in 40 minutes, being fun and legal/acceptable.

I see three answers saying "Just don't do that" with variations. They may be right. Nevertheless, I would like to suggest another answer.

Slow down!

Seeing a bike coming towards you at full speed is indeed scary. You should try to avoid scaring people.

If you slow down to walking speed, the scare goes away. By going slow, you both indicate that you are in control, and also the consequences of a collision would be much less.

If you can see for a fair distance, slow down well in advance of meeting pedestrians. If you can not see well, just assume there are pedestrians and slow down anyway. In fact, assume that small children are playing there and deliberately trying to hide from you.

If the staircase is really narrow, you might want to stop entirely and let them walk past you. You can squeeze closer to the railing that way.

... or find another path.

because I have no problem stopping

Objectively, this is nonsense. At best, you can stop before you start going down the steps. Once you start going down steps on a bike though, you are completely unable to stop before you reach the bottom, and you have very limited control over your speed whilst you're doing it. And that's assuming you stay on your wheels. If you catch a bar on the wall, skid on a damp surface, or simply lose your balance, you're going to wipe out directly into whoever's underneath you.

Anyone going down this on a bike would be a perfect example of why so many pedestrians think of cyclists as arrogant, selfish, dangerous idiots - because this would be arrogant, selfish, dangerous and idiotic. You prevent this situation from happening by not doing it.

Always remember the golden rule of doing tricks. Hurt yourself trying it, you're a hero. Hurt someone else trying it, you're doggie doo-doo (censored :). If you want to have "fun" going down steps like this, station a buddy at the bottom to let you know when the stairs and approaching paths are clear. Then do your stunt and move on.

Its highly advisable that you do not ride your bike down a narrow staircase where pedestrians are present. People will get very mad with you, and it very likely could be against the law/city ordinance. Additionally, you could be destroying or damaging the stairs by doing this. Either walk your bike down, or find an alternative route. Hope this helps you make the right decision!

Being myself somebody who rides down various stairsets pretty much daily, I obviously disagree with the answers stating that this should categorically not be done.

However I do agree that it's a no-no to ride down a narrow stairset when there's someone below you, or might appear below you. I.e., I only start descending if I can oversee the landing, and know for sure I'll reach the bottom before anybody else can reach the stairs.
Could I slow down or stop on the stairs, if somebody appears out of thin air? Probably / it depends – on stairs that aren't super steep this is indeed perfectly possible. But it's not reliably possible: a slight imbalance, slippy surface, unexpected brake response, and you can quickly find yourself going much faster than intended. Now, it's one thing if this leads to a crash involving only yourself and a wall. It's an entirely different thing if this leads to a crash involving somebody else.

A bit of a corner case is if it's a stairset consisting of multiple flights in a row. I suspect this is in fact the situation you're talking about. In such a case, if the flights are separated by at least 4 meters of flat ground, I'd say it is safe that you can stop there even in adverse conditions (in the worst case, by crashing), yet somebody coming up the next lower flight could very well be scared by the prospect that you might not stop but just thunder down the entire thing.
In this case, my advice is: stop immediately when you see someone, and either wait to let them pass and then continue the fun, or else switch to carrying/pushing the bike the rest of the distance as per Jahziel's answer.