Video hosting providers
Watershed from Ustream offers Pay as You Go Pricing starting at $1 per 'viewer hour', where 60 plays of a one minute video cost you $1. PAYG pricing is generally much more expensive and can feel like signing a blank cheque, but it might suit you to begin with if your videos are short. Just keep a close eye on usage and consider migrating to a monthly package at $49 for 500 hours (potentially saving $451/month).
Vzaar doesn't offer PAYG pricing, but their basic monthly plan at $49 for 50GB of playback bandwidth seems reasonable. It's hard to compare bandwidth-based pricing with viewer hour pricing, but you could estimate it by calculating the size of a one-minute video using whatever compression method you adopt.
Vimeo Plus offers a great service for $9.95 a month (or $59.95/year), allowing you to control what domains videos can be embedded on, upload up to 5GB of video a month (no mentioned cap on monthly bandwidth or total storage), customise the video player, prevent your video appearing on Vimeo.com (great for member-only sites) and more.
Do it yourself solutions
An alternative is to host your video files on Amazon S3 or Amazon Cloudfront, then use a Flash media player such as Flowplayer for playback. Amazon detail the setup procedure here, and there is sample code in the Flowplayer forum that shows Flowplayer working with Cloudfront. Again, you'd need to estimate pricing based on file size and bandwidth, and compare Amazon's pricing with other CDN services, such as Rackspace Cloud Files.
Which to pick?
If you have a lot of time and technical expertise and money is tight, I'd suggest hosting the files on Amazon and rolling your own playback solution. If you need to get something up fast and can afford the monthly fees, or you don't have the skills or inclination to roll your own solution, pick one of the video hosting platforms.
Also consider that, while DIY solutions can seem tempting if you're a programmer, they often turn out to be false economy and giant time sucks for an agile startup. Sometimes, it's better to splash the cash and get the darn thing launched. If I were bootstrapping a video learning site, I'd pick Vimeo Plus and spend my time marketing instead of programming, then move to Brightcove or one of the above mentioned alternatives if I outgrew Vimeo.