Sign in, click the 'Upload' button, click 'Choose photos & videos' button, select pics you want to upload, click 'Open', and the pics will upload to Photobucket. Create an album first if you want to keep groups of pics together in one place and upload into that. Done.
When you want to post pics on BassChat, select the pic you want on Photobucket, choose the 'Direct' link from the list on the right, click on it to copy the link, then go to the post editor on Basschat (where you type your post in), click on the green 'image' square (above), paste in the link and click 'OK'. You should see the pic in your post.