Many other Pixel editing programs can do this conversion.
I often use XNVIEW (freeware) as a file browser, which has a simple menu- "Convert into"
I tried two images and it 'Batch' converted them both.
And- If you have Photoshop-
1. Open a BMP image
2. Create a new ACTION: (that Saves as JPG)
3. Run a batch conmmand on a folder of BMP files with the action. (Menu > File > Automate > Batch. Selecting the 'Save as JPG' action.)
Yes I do have PS. This is great