My question is: Should I keep slowly boostraping or should I start talking to angels? What other benefits besides money does a good angel have? Should I care about his connections or will the product sell itself if its good enough?
If you're able to bootstrap your way through your private beta, do it. If possible, I'd hold off talking to angels until you've found a repeatable, scalable customer acquisition processes. If you manage to do so, you'll be in a much stronger position with the angels, and you'll also have a clear idea on how to effectively use the money raised.
Remember opportunity costs-- the time the OP spends (wastes) talking to angels when he doesn't need money is time taken away from more productive pursuits (building the product, acquiring customers, etc.)
Presumably your repeatable, scalable customer acquisition process will be bringing in lots of customers, who in turn will bring in income. So, you won't much need angels for money.
Also, the fact that you have a repeatable, scalable customer acquisition process means that you've solved one of the most, if not the most important problems a startup faces. So, you won't much need angels for the connections and advice on how to increase your traction.
Of course the above is over-simplifying a bit. Even with income and more and more customers signing up, you may still need money to expand at the rate you want. Still, once a startup finds a repeatable, scalable customer acquisition process, it's hard to see much need for angel investors.
I disagree. What's more, I think you do, too. You said as much a sentence earlier: Even with income and more and more customers signing up, you may still need money to expand at the rate you want.
If you've got a repeatable, scalable customer acquisition strategy, more money in means more customers (and profit) out. In other words, you've built the money machine-- now you use angel money to get it running full speed.
You'll find a wide range of personal suitability (connections, meeting of the minds, smarts about your space) in the meetings, so definitely worth doing.
Now, if your product doesn't need money because it's paying for itself, then you DEFINITELY should go talk to investors a) because you'll come away feeling awesome about yourself, and b) because you'll be able to command some truly awesome pricing.
EDIT: So my answer is yes, you should start talking to them.