Resize is the tool you need. It is the simplest way to convert any kind of files to the filesize you want.
Resize supports BMP and JPG formats.
It is really easy to use, you only have to choose the images you want to convert and the conversion formula you want to use. You can do it by selecting a percentage or selecting the width and large you want. You will be able toc hoose the JPG image quality too.
In addition, it doesnt have to be installed and is totally free.