You can now share Bandcamp players directly to Tumblr, and they’ll look great on both your blog and the Tumblr dashboard. Just head over to any album or track page, click Share/Embed, click the Tumblr button, et voilà:
The far less important detail: if you prefer our standard or small layout player over the horizontal layout that the Tumblr button produces (or you just want to customize the colors of the horizontal player), it’s possible but requires a bit of fiddling. Go to https://www.tumblr.com/settings and temporarily switch your “Edit posts using” setting from “rich text editor” to “plain text/HTML” (Tumblr’s default rich text editor strips some of the attributes from the iframe tag, which causes the player to clip). Then click the Share/Embed link back on Bandcamp, choose “Embed this album,” and go to town. The catch is that players you embed this way will not appear inline in Tumblr’s dashboard view, whereas the players you get when you just click the Tumblr button do.