The move comes as Chicago arrives at the ballpark following a 9-2 win on Friday to open the weekend series with Oakland.
Bido has appeared in six games this season and is 1-0 with a 6.30 ERA before joining the White Sox, adding another arm to the bullpen for the weekend slate.
The club confirmed the acquisition on X (Twitter), noting that Bido was claimed off waivers from Atlanta and that Berroa was moved to the 60-day injured list.
Bido’s MLB career began with the Pittsburgh Pirates, then spanned two seasons with the Athletics before his stint with the Braves. In 64 career MLB appearances, he is 10-13 with a 5.13 ERA.
The addition provides Chicago with added bullpen depth as it faces the Athletics in Sacramento this weekend.