Is it better to approach companies that you think would buy you out, or let them find you on their own?

I am working with a couple of people and we have created some software which, despite being a strong stand-alone, would be even better if integrated with another existing product. This has always kind of been our endgame.

So my question is, is it appropriate or even a smart idea to approach someone by whom you're hoping to get bought out, or let them find you when you're [potentially] more well-established?

This is quite the dilemma. If you approach the company, they are at a strategic advantage because they know you're interest and thus they can play you down. However, if you wait for the company to approach you, they may not notice or approach you.

That being said, you could do as Manny suggested in the comments and consider partnering with the company or licensing to them. Once you have something like that in order, it's possible that the company could approach you about an aquisition or you could bring it up. Either way, you'll have a stronger position to negotiate given your partnership or whatever you have worked out.

If you're set on having the company approach you, yet it seems as though they haven't noticed you, you could try:

1. advertising locally around their main offices(ie: Television ads, billboards, etc in the city of their main office. The execs and other decision makers will most likely see these ads and could become interested.)
2. advertise online for some of the same keywords as they are(ie: in google adwords). When their PPC traffic is down for the quarter, the high-ups will ask their PPC marketers why their traffic is down and they'll say that your product has been ranking with/above their advertisements.

hope this helps and best of luck!