According to Official Guinness Records,
The most bounces of a soap bubble is 195, and was achieved by Kuo-Sheng Lin (Taiwan), at Hold Enterprise Co. Ltd. in Taipei, Taiwan, on 17 April 2012.
Lin used bubble solution from Hold Entreprise Co. Ltd. (a bubble manufacturer) who also hold the record Most soap bubbles blown inside one large bubble and most soap bubble domes. He wore a glove on his hand to assist with the bouncing.
For a complete list of 2012 records, please visit 2012 Guinness Records in Taiwan.