The most versatile and powerful program is Adobe Photoshop, but the full version is quite pricey. I have used it daily for years, but have always had the good fortune to have the program on my work computers.
There is a consumer version called PhotoShop Elements, which is a slightly more basic version, but with all the features needed for the home user.
You can find more information about it here: http://www.adobe.com/products/photoshopelwin/
Please note that if you are converting photos to JPG they will be compressed, and the higher the comression is the more lossy (blurry) the picture will become.
I don't know how familiar you are with digital photography and photo editing, but if you are going to be opening, editing and saving photos over and over again, I suggest using a format like .tif or if you need it to be JPG have save at high quality.
Of course it also depends on what you do with your photos. If its just for screen display, you shouldn't have any problems with JPG. If you need more info about this just let me know.
If all you need to do is simply converty a BMP to JPG, you can use this nifty online conversion tool: http://www.coolutils.com/Online-Image-Converter.php
Best, Itay.
