There are two very important factors here: (1) your psychology and (2) the psychology of the person you’re speaking with.
If you are comfortable with making mistakes, you will be able to speak much earlier. And if you find a conversational partner who enjoys talking with someone who is not an expert in the language, you will be able to talk with them much sooner than with someone else.
However, I think our psychology in this area is pretty much fixed by the time we’re adults. It’s hard to get yourself to switch from being a self-monitoring type to a free spirit just by giving yourself an encouraging talk. And it’s pretty much impossible to get someone who does not already have the characteristics needed to speak to a non-native (patience, fascination with language, understanding of one’s own language, clear speech) to acquire them on the spot.
Having said that, two people can grow together as conversational partners. I’m thinking of someone at work who used to drive me crazy because he spoke so quietly and because when I didn’t understand him, he would switch to English. However, over time, I became a better Hebrew speaker, and he became more willing to stay in Hebrew when talking to me. He really understands his own language, and enjoys language-learning himself, and these traits helped me overcome the fact that he speaks quietly. Also, we know and like each other and have a lot in common. Striking up a conversation with a stranger who may or may not be interested in “small talk” is a very different matter.
Another way to look at it is that with time, the number of people you can talk with, and the number of people you can understand, will increase. If you can find yourself a good conversational partner to talk with on a regular basis, you’ll get a feeling of satisfaction that will make you stop worrying as much about how long it will take you to get to the point where you can talk to just about anyone. Another thing that will get you through is your ability to take pleasure in your growth in all your language skills other than speaking, since that could well be the last piece to fall into place.
As for quantifying how long it takes, that depends not only on the first two factors, but also on the “difficulty” of the language (how different it is from your original language), as well as many other psychological factors. I wouldn’t feel qualified to guess how long it would take you to get to the point where you can speak Romanian with anyone you want.