Bowden cleared waivers and was outrighted to Triple-A Durham on Saturday, Marc Topkin of the Tampa Bay Times reports.
The 27-year-old was designated for assignment Tuesday to make room on the 40-man roster for right-hander Shawn Armstrong, but Bowden will remain in Durham after going unclaimed on waivers. Over nine relief appearances in Durham this year, the southpaw has posted a 1.80 ERA and 1.60 WHIP in 10 innings.