Eh is this possible? Just downloaded the Photobucket app so i have a direct link...
Do you mean image uploading to Wiki articles or the forums?
If you are a premium subscriber you can access a mobile-friendly HTML5 version of the website. I don't think it gives you a way to upload images to the forums, though it might help you with that when it comes to wiki-editing. However, if I had to guess I'd say you'd probably have to upload images to the site by submitting an image URL. But I don't know.
Since you're not a premium member I guess you should just try uploading images using this version of the website.
Oh and if you don't want to upload a picture every time you can do another HTML code.
Type "<.img .="" src="IMAGE URL"><.>" That would post the pictures. Without the periods or the quotes there. Keep the middle quotes. Then just paste the URL of the image in image URL.
If you want to basically click enter on a iPad on the site, type <.p>. (Without the period) Then that would create a line. As so:
type two in a row and space!
So yup. I've been doing this a while on my iPhone.
The only way to upload images to the site is via the Flash-based uploader. You can't use it on an iPad because Flash is not available for iOS (and it's no longer available for Android either, for that matter).
If you don't want to upload and just want to embed, then use the embed code like SexyToad said.