It won't cost you that much, because you're almost certainly not going to be successful as Instagram or Twitter. If you are, you have what is called a "high class problem."

Here's a less stratospheric comparable for you: I run a business with something like 250k users and 10~20k monthly active users, with those numbers representing people with accounts. The costs to run the business are do not scale linearly with traffic, at all. I spend about $300 a month on hosting (VPS at Rackspace) and bandwidth and another few hundred bucks on various recurring things (server monitoring, analytics solutions, etc).

The overwhelmingly likely source of failure for your application is not that it will bankrupt you with hosting cost. It is that you will not be able to convince two dozen people to actually use it. This should be the worry that wakes you up screaming in the middle of the night and causes you to go get advice from people you think are credible. It is far and away your largest source of risk. Pick any population of startups which you admire: their #1 scaling problem is that they have no scaling problems at all!