What's the model number? There are a few different models and IOS versions. Jumping from 12.2(25)SE to 12.2(55) won't be an issue.
You shouldn't really just use the .bin file. Get the .tar file and use the 'archive download-sw' command as this will configure the boot parameters for you and copy the HTML files for the GUI management.
According to the release notes the WS-3750G-48TS supports 12.2(58)SE1 and later releases. You can therefore upgrade this to 15.0(2)SE11. It is the same image for the 3750V2 series. This is the final release for this switch as its EoL.