These birds/bugs use the same code as floating items. So every page there is an x chance of finding the floating item, so sometimes it'll be really easy to find the bird because you've got luck on your side and other times it might take ages. Just continue to browse the site! Do things that require a lot of pageviews (quests, posting on the forums, etc) for the non-regional. If it's a regional, just stick around and click all the areas in that area.

If you don't already, maybe use the customCSS that makes the item appear in the corner of your page so you don't accidently miss it on a page further down. :)

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forgot to mention, i mean if you really want to give up on the finding the bird (like say it took 6 hours or something and still no bird), you can buy one from user shops and show it to her. :x