My area of expertise is primarily on the Malayan Campaign so I can't really speak for say the Sino-Japanese War or the Japanese capture of the Dutch East Indies. The Japanese army in 1941 at the time of the invasion of Malaya was significantly less motorized compared to the British army. The Japanese had relatively few vehicles supporting their infantry while the British by that point had access to a sizable number of trucks and Universal Carriers. Thus one easy way to overcome their lack of mobility was to use bicycles to augment the speed of their leg infantry.

The Japanese invasion of Malaya was constrained due to the lack of ships to carry out the landings as it occurred simultaneously with the Philippines Campaign. This made it such that there was a limited amount of equipment that could be brought with the Japanese forces to the peninsular before their land supply routes opened up through Thailand. In addition there was also an extensive lack of fuel throughout the Japanese Army with fuel reserves largely being allocated to the Navy and the Aviation Services making the use of vehicular transport problematic as there would be no assurance that they could be resupplied. Bicycles were thus the preferred method for General Yamashita to increase the mobility of his troops for his drive down the over 700km long Malayan Peninsular as they required little supplies to sustain.

Japanese intelligence had made a breakthrough as they had reliably ascertained that the Malayan Peninsular had an abundance of civilian bicycles. Thus General Yamashita elected to have his troops deploy without bicycles and then capture the civilian ones available on the peninsular in order to reduce the store they carried reducing disembarkation time. Bicycles in the campaign were particularly effective as contrary to popular belief most of the campaign was fought on the roads running the length of the peninsular and in the adjacent jungle as opposed to being fought in completely rough terrain. The bicycles gave the troops a mobility advantage on the road network allowing them to continue their advance and keep the British off tempo by utilizing the road network.

In conclusion, the bicycle was a readily available piece of equipment that required little supply or maintenance that significantly improved the mobility of leg infantry. Thus the Japanese Army chose to utilize it due to the advantages it presented to them in light of their own limited ability to muster motorized transport.

Sources:

Singapore Burning: Heroism and Surrender in WWII - Colin Smith

The Defense and Fall of Singapore - Brain Farrell

Japan's Greatest Victory, Britain's Worst Defeat - Masanobu Tsuji