(disclaimer: not knowing what your product does nor what your customer group is, this will be a more generic answer)
This is very often an incomplete stage of the cycle and IMO will require experienced testers that is familiar with the development process as there could be missing some functionality. Ideally alpha-testing should be done in-house or by a small group of people not necessarily associated with the companies you're targeting - as it is much a technically and operational oriented testing.
In other words: bringing an alpha version to potential future customers can fail as they, in general, are not fully familiar with the development process and it can leave them with a negative impression of the app. Alphas are too incomplete to bring outside IMO.
Now the application is complete in the sense of functionality and bugs are to be found and removed. IMO this is the stage where you should involve a few select potential customers. It's easier to get apps at this stage tested as everything is in place and bugs are the focus, not so much functionality. But not without an internal initial beta-test to catch the most obvious bugs.
To pay or not to pay
You are asking people to do work for you. Charging them would be wrong in my opinion. For businesses to spend resources/time on doing testing for you would make them want something in return. Maybe you can offer them 50% for the first year, free first two months, free setup (something more in terms of what you deliver) and so forth.
As they already have spent time on your product and are getting more familiar with it, they are more likely to continue with it if they think of it as a good product. See the compensation as a sales investment. As you work closer with customers that do testing you can also get valuable references/case-studies to use with future customers.
Make it a win-win.
In my experience people tend to say yes to do testing as it initially makes them feel part of an exclusive group, ie. have access to something that not everyone has access to. The reality bites when they discover they need to sit down, spend time and work with an incomplete app that may give unpredictable result, or even loss of work (if that applies).
Finding the right person to do testing is not always easy, but if the company has an "evangelist" (s)he can often be a good starting point to either test or help find the right persons for you to do the testing.