If there is public transport connecting your start and destination points, you are likely to be able (and to be allowed) to travel with your baggage. A regular disassembled bicycle is such a baggage. It is rather bulky (resulting dimensions are defined by the diamond shaped frame) and heavy, but not outrageously out of reasonable limits.
There are usually regulations of how long/wide/deep a piece of baggage can be, and it is usually implied that you must be able to carry it alone without help. Check with your transport authority on what rules are in your city/country. Sometimes you'll have to pay an extra fee for your baggage; often you can avoid it, especially if you do not focus anyone's attention that it is a "bicycle" you have with you. Be focused that it is not a bicycle, it is just baggage, and you are allowed to have baggage with you.
Then, the key is to pack it down as compact as possible and to protect it from damage as well as reasonable. Here are several suggestions that help me to pack my current "adventure" 28" bicycle when I travel by bus (or by train, that one stupid kind of train that does not allow bicycles…)
- Take off both wheels and strap them to the middle of the frame from both sides with e.g. bungee cords or zip ties or any sort of rope.
If there are discs on wheels, keep them closer to the frame in order to minimize risk of bending them. Alternatively, remove the discs for transportation. Do not deflate wheels if possible.
Taking off the wheels is the biggest space saving action. Sometimes only the front wheel should be removed, and the rear stays, it depends on your limits.
Put some sort of spacers between front and rear dropouts, where the hubs were. Wooden blocks of 100 mm front and 130/135 mm back can be drilled to serve as "dummy hubs". This will prevent side loads from bending your fork and frame. Other types of spacers (plastic or bamboo tube, basically whatever you have at hand) will work as well.
Unscrew the rear derailleur from the hanger and strap it to the dropout with a wire, electrical tape etc. Without the rear wheel, the rear derailleur is protruding and is at high risk of being damaged.
Lower your saddle in the frame to reduce height. Alternatively, extract the seat post and hide it inside the front triangle.
Loosen and rotate your handlebar (if drop bar) or even detach and zip tie the straight bar to the frame to further reduce dimensions.
Detach pedals in order to reduce width.
To go at the full extreme, extract the fork and tie it to the frame. Be careful to not loose any of headset or stem parts (because of that, I actually do not recommend detaching the fork).
Find or make a cover to wrap your neat package. They are usually cheaply sold, or can even be custom sewn to fit your bike. A cover can be very light and does not need to provide any protection from strikes. Instead, it makes your baggage to look just like a bulky bag with no sharp chainring teeth sticking out anywhere.
If you will be controlling (e.g. holding the bike) the whole time, I would say that points 1, 2 and possibly 3 are mandatory. If anyone else will be handling your baggage without your control, further disassembly and protection steps are desirable. Having a cover helps to keep everyone clean and happy.
It may be worth mentioning a "proper" method to travel mass transit with a bicycle (with its own deficiencies).
People do travel with bicycles even on planes, sending them as checked luggage. Special hard-shell cases exist to put the bicycle into.
These bags do offer better protection under travel, and even have their own small wheels to be rolled around an airport just as a usual case. As expected, they are rather expensive, especially if you do not travel often with your bike, to the point that I see people renting such travel bags instead of owning them. They are also still bigger than regular biggest travel case, which, in certain countries and with certain companies, incurs additional baggage fees.
A few final remarks and suggestions.
- Avoid rush hour when carrying your baggage.
- Make sure you can actually lift and carry your baggage. Find places on the frame that you can grab onto and lift.
- Be gentle. An assembled bicycle is very resilient; without wheels it is rather vulnerable. If you intend to carry the frame upside down, put some protection cover onto the saddle to prevent scratching it when you put everything on the ground.