The reason why Japan does not have garbage bins is because of a sarin gas attack that occurred in 1995, that occurred on the Tokyo Subway as well as because of a cultural emphasis on personal responsibility for trash.
Ever since the sarin attack in 1995 on the Tokyo Subway, many trash cans or garbage bins were removed from any public spaces, particularly from transit stations, as the Japan government still views the garbage cans as potential terrorist tools, which is also reinforced by a societal norm, that expects people to take their trash home with them and not be a burden on public spaces.
The 1995 sarin terrorist attack on the Tokyo Subway, was when chemicals were released from containers hidden in trash cans, which prompted the removal of the garbage bins from stations as a security measure.
The initial security measure of removing the garbage bins, became a lasting feature of Japanese public spaces, and many cities and private organizations in Japan still view them as a potential security risk.
And security measures, like locking or removing garbage bins are also often implemented during state visits and special events.
Also from a young age in Japan, people are also taught to clean up after themselves, and this is also reinforced in Japanese schools as well as daily life and has also led to a public in Japan that is largely accustomed to taking their trash with them.
And in Japan, there is also a strong societal value of avoiding causing any trouble or inconvenience to others which is called "meiwaku" in Japan.
And so having public garbage bins in Japan, would also be seen as a convenience that could also lead to others having to deal with the trash, which is an idea that runs counter to the Japan's values.
To throw out a bed or other bulky waste in Japan you have to arrange for a bulky waste pickup also known as a sodai gomi through the local city office.
The process of arranging for a bulky waste pickup to dispose of a bed or mattress or other large waste involves contacting the city in Japan's oversized garbage reception center for the city of Japan that you're in and scheduling a date, purchasing a sticker or ticket also called a sodai gomi ticket for the required fee from a convenience store or supermarket and placing the bed at a designated spot on the correct morning with the ticket attached to the bed or other furniture you want to dispose of.
Some people in Japan have cut up a mattress and disposed of it bit y bit, although it can take months to throw the mattress or bedding away bit by bit.
So the easier and faster way of disposing of the bulky waste or mattress in Japan or bedding in Japan is to schedule a pickup, through the bulky waste pickup.