You're actually in a similar position to most small businesses that start to consider an exit - you've never really needed to build relationships with potential purchasers, and so you haven't.
The fact that yours is a website gives you some advantages (potentially global purchasers, depending on your product) and some disadvantages (many of those small businesses sell to their staff, which you don't have or need).
To get the word out, you do need to make some approaches and build some relationships (start building out who you know - it's a very useful skill, if only because it scares most of us so we avoid it).
As a broad suggestion, look horizontally - who are your competitors or very similar businesses operating in the same space. They may see you as a successful acquisition; then look vertically - what do your paying customers buy shortly before or shortly after your service, because those businesses can readily expand into your market through your acquisition.
Approach them to discuss the market in general, the opportunities they see etc. This is all excellent research, and with the right people (ones you feel comfortable with) you can start mentioning your plans to pursue 'other projects' or even 'outright sell'.
This isn't the only way to sell your business of course, but it's a smart place to start.