if you can upload pics to photobucket and not the blogger account, then it isn't the b/band that's causing your problem. Unless there's a max wait for uploading pictures and it's the slow speed of the b/band that's causing the problem. Either way, you cannot get around the upload speed issue of your network unless they can increase the upload speed.
Or maybe it's the size of your pics that's preventing upload to blogger???
I have issues sometimes of uploading pics to fb because my wireless b/band is so.... slow. That I give up before allowing it to finish the upload.