According to Official Guinness Records,
The fastest time between baselines dribbling a basketball was 3.605 sec by Arve Gravdal (Norway) at Stavanger Idrettshall gym in Stavanger, Norway, on 10 December 2010.
Gravdal broke this record after it was set by Gregg Farrer (Norway) at the same event only minutes before.
For a complete list of 2010 records, please visit 2010 Guinness Records in Norway.