Yes you can, but don't use the Photobucket app as it's crap.
Assuming you've already got a Photobucket account go to their website
http://photobucket.com/ and login.
You will be able to select an existing photo from photos already uploaded.
Alternatively click on Upload (blue button top-right corner) and then '
Choose a photo or video'.
At this point you can '
Take Photo or Video' using the iPad camera or pick something already on the iPad by selecting
'Photo Library'.
Once photos are uploaded into your Bucket click on the link icon (a couple of chain links joined together), move down to the 'Direct' line which contains the code for the direct link to the picture. Highlight before the 'h' in 'http://' at the beginning of the line and then touch again at the same spot. Touch 'Select All' and the 'Copy'.
On another tab in Safari browse to the forum.
You can try linking to a picture using the 'Insert Image' icon...but my iPad crashes Safari at this point.
It's easier to type [IMG]then paste your saved URL by holding your finger down directly after the ] and selecting 'Paste' and then closing it with[/IMG]
...leave no spaces before or after the URL.
Please note: I have nothing but grief with the 'Insert Image' button on iDevices within this site and the Apple iStore Photobucket app (IMHO) is crap. Your mileage may vary but keep in mind what I've told you as it's a right royal PITFA