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 Medeiro. 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.