Self-Hosting an Application

Can anyone clarify
Is it possible for Self-Hosting an Application which developed in Bubble ???

All apps created in Bubble are contained and hosted within the Bubble ecosystem. So no, in it’s current state you can not self-host or pick any other host than what Bubble provides. Nor is there any export of the design or workflows of the app.

Bubble offers several kinds of hosting though, included dedicated servers.

How would that impact security? Let’s say you have an app where users would store sensitive financial data. Wouldn’t there be risks to the users, if you could not tell them that the entire ecosystem was under your control?

Well, the short answer here is that Bubble is not really meant for apps storing sensitive data. That’s not to say that Bubble isn’t secure, but that apps with highly sensitive data (say an online bank or a hospital) use a lot of resources securing and auditing their solutions - everything from software to hardware. It depends on your definition of “sensitive”. Bubble is secure enough to keep data for an ecommerce store, a CRM or an HR application, but we won’t be seeing any banks built on it in the foreseeable future. That would require security on a level that Bubble really has no good reason to implement, and it would demand a lot from the Bubble developer to actually keep the app secure within the Bubble ecosystem too. This is not actual statistics, but I don’t think it’s unlikely to say that 999 out of a 1000 breaches of a Bubble app would be the developer’s fault rather than the platform.

For the last part of your question, I’d agree that yes, there is a risk not knowing the entire ecosystem of your app if it handles sensitive data, and if I were a client, I would probably question the use of Bubble in that case.