do I have other options?
If there's one thing you have when it comes to hosting, is options. There are plenty of hosts out there.

I need the bandwidth so hundreds can play the video at the same time but don't want to pay more than $50 a month.
Something doesn't really add up. If you really expect hundreds of people downloading your files day in and day out, shared hosting is not what you're after.
Just to run a few numbers, lets assume you get one of the low priced, overselling fueled shared hosting packages out there, that comes with say 1TB of data transfer. That means you'll be able to serve 50 times more videos that you can right now. That comes to 100,000 downloads per month. Dividing that evenly over a 30 days period comes to ~3000 downloads per day, or ~130
per hour. That's just over 2 downloads per minute. Not anywhere near the hundreds you predict.
With my current host, I am paying 39.00 a month, 4 gb and 20 gb monthly transfer.
It sounds to me like your current host may be targeting webmasters who host application heavy websites (typical ecommerce sites tend to be that way). Yours on the other hand is (potentially) file transfer heavy. Your site won't need high amounts of server resources (CPU power, memory), but need as much data transfer as you can get (maybe not as much as you're assuming right now though).
Personally, I think you're heavily overestimating your site's traffic, especially considering that only those who are willing to pay will get access to the extra files.