The Time Bubble was invented by Brainiac 5 as a child. The reason for this differs by continuity, pre- crisis it was to meet his crush, Kara Zor El as he knew of the early death that awaited her. Post- Infinite Crisis Brainiac's childhood work on the Time Bubble was so benefactor RJ Brande could prove Superman was more than a myth. In both version this work is done prior to Brainiac 5 joining the Legion and when he was in the employ of Brande.
In Superman and the Legion of Super-heroes it is revealed that despite a time bubble being broken into small bits, it takes a short time for Brainiac 5 to fix. This is a modification that has taken several years since its initial invention. The Time Bubble is far more durable than other forms of time travel equipment such as the Cosmic Treadmill of the Flashes which was obliterated when in a collison with Rip Hunter's bubble. It also lacks the side effects of Rond Vidar's Time Cube, a technology that did the same as the bubble only it was portable.
During an encounter with the Doom Patro l in Brave and the Bold we learn time bubbles are TARDIS-like. This explains why the Legion could fit expansive lab equipment into the confined bubble in early stories.
By the time Brainiac 5 had joined the Legion he was perfecting personalised time travel that he used in Supergirl Annual #2 to thrust he and Supergirl days into the future. This line of research appears to have not led to a device more accurate and efficient than the time bubble.
The Time Bubble is an important piece of equipment for Booster Gold. It transports Rip Hunter and the Carters around the time stream to fix the anomalies present after '52'.