Hi there,
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Bubble provides the hosting for you with the Bubble application. Its included within the free and paid plans with different perks depending on the selected tier. Note, its currently not possible to self host a Bubble app/site.
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There are a number of posts on the forum that cover this topic. Its currently not possible to make a true native app through Bubble, you can go the hybrid route. There are external sites or plugins that will enable some native capabilities. See these resources below:
http://forum.bubble.io/search?q=make%20native%20app
Hope that helps.