I work on the public sector and have developed a web app for internal use to handle a department's business process. The application has been a success according to its users. Some of the users are internal employees, some are consultants.
The consultants showed the application to their superiors and they came back saying if there is a way they could purchase the application, as it would be beneficial for their consultants that are scattered around other companies with a similar business process.
It turns out that the legal hoops that we have to trough to sell the application are too complicated because we are not a software shop that sells software.
So my questions are as follows:
My goal is to be able to keep my current job (benefits and pay are great. Work is pretty good, 8 and out and no pager) but start this on the side and go solo when it takes off.
If I do question #2:
At the end of the day, go talk to your boss. S/He will probably send you a couple levels up or to HR/Legal for a discussion. Take your time and be patient while working through this.
It doesn't hurt to ask. However, bear in mind that one of their concerns is going to be on your focus with the company as you start this ancillary business.
In the negotiations, you might consider offering free updates to your current employer as you build the app out.
BTW, in the past year I've had two employees start businesses. In both cases they approached me and let me know what they were trying to do. Neither were competitive, one was complimentary to our core focus. Not only did I give them "permission" so to speak, but I also actively encouraged it by being more flexible in work schedules. Both employees were so excited I'm pretty sure productivity went up.
Unfortunately, neither took off. One had problems with a product they were having made in a foreign country; the other idea was killed by the market.
Personally, I think it ended up being an overall win for everyone. They got experience in trying to get a business off the ground in a "safe" setting, which will help them for the next go around. I got employees that understand a bit more about the complexities of running a company as well as actionable ideas on how we can be more effective.
good luck to you.