Bart is one of Calvin's clones, and is Bob in Residence in Alpha Centauri manning the "Bob factory".
Bart's VR is a rustic log cabin with lots of rugs and blankets, and a cast-iron, wood-burning stove. It has handmade furniture that is sturdy, including a large rocking chair modeled after the one that original Bob's father had spent a lot of time using when he would take the family on vacation to a similar spot.
Timeline[]
When Bob creates his first five replicants, it takes him nine months before all are complete (September 2144 - July 2145). Calvin and Goku arrive in Alpha Centauri in November 2163, and spend about a month on their mission against Medeiros. They then set about building new probes.
Based on this, Bart would have woken up in his vessel in September 2164.
Assuming that the replication effectiveness has been improved by 2163, and that building one probe is faster than building five, his date of creation is probably some months earlier than this.