It’s only a matter of time until a spoke will break while riding out and about. There’s no way around it. Now comes the question of whether you can ride a bike with a broken spoke.
You can continue riding home without any concerns. Having a broken spoke will not make any lasting damage to your rim for that short period that takes you to go home or to a bike shop. Be sure to secure the broken spoke by curling it to another spoke for you to not hurt yourself.
Why do bike spokes exists?
Spokes are the connecting rods between the bicycle hub and the rim. Their main purpose is to transfer the loads between the hub and the rim, which are caused by the weight of the rider and the bike.
Quote taken from here.
Anatomy of a bike spoke
The side of the spoke that is bended. This end is connected to the hub. 
The side of the spoke that is connected to the rim using treads and a nipple.
It’s connected to the rim with the use of a threaded nipple. The other part of the spoke is connected to the hub with the spoke having a J shape for it to come and connect from the side.
Wheels can have different spoke patterns. The most popular ones are 3-cross, 2-cross, and radial. There’s a great article you can read here about the different patterns.
How many spokes are there on a bike wheel?
Depending on the bike type you own, a bike wheel can have 28, 32, or 36 spokes. The weight of the rider and the bike are an important indicator of the number of spokes. Tandem bikes can have 40 or even 48 spokes.
How do bike spokes break?
Fatigue is what will break a bike spoke. They are made from steel as they need to stretch from the tension. At some point, after millions of wheel turns, it will break. Of course, aggressive riding and jumps will decrease the time a spoke will stay intact. The most common areas of breaking are at the ends of the spokes, not in the middle area.
How much does a replacement cost?
The cost will differ depending on what side of the hub is the broken spoke. You may need a special tool to remove the cassette or disk break to get to it.
How to fix a broken bike spoke
There’s a slight chance fixing it will be simple and straightforward. If the hub is not obstructed and the nipple is intact, you’re in luck. With a few dollars and a couple of minutes of your time you’ll have a wheel good as new.
Be careful when buying spokes, the length differs, so be sure to measure one from your bike to know what to get. Another thing to be careful about is that spoke nipples differ in size. So be careful when buying one and choose one with many sizes if you don’t know which to buy.
If the nipple is damaged and needs to be replaced, the process is greater since the wheel, inner tubing and tape need to be removed to get to it. You also may need to true your wheel after this process which requires another tool or some DIY hack. A DIY method can be seen at the end of video.
Going to a bike shop is always an option, so consider that knowing it’s a lot of work and requires several special tools to fix it yourself.
How to temporarily fix a broken spoke
You can prepare for this misfortune in advance. Always have at you replacement spokes to fix on the go and replace it for good. An alternative would be to have a Emergency Spoke Replacement Kit to have a temporary fix until you get home or to a bike shop. Whatever you do or do not have at you, be sure to secure the broken spoke to another good one for you to not hurt yourself with that loose wire.
Can you ride a bike with 2 broken spokes? What about many broken spokes?
Three broken spokes would be the limit at which your wheel will start deforming. So don’t postpone replacing the missing spokes forever, it will become costly fast.
If you have more than 3 spokes broken, your wheel will need truing, so consider going to a bike shop.
Conclusion
You shouldn’t have any concern when riding a bike with a broken spoke. It will handle the burden until you will get home or to a bike shop with no issues. Fixing it at home may need several special tools, which is not ideal for a simple task, so consider going to a bike shop.