Trust is like an elevator cable, in that only its absence should be remarkable. Trust between provider and consumer isn't something you must only "build," it's something you first earn, then maintain and preserve. Saying you can "build" trust implies that you can move from a position in which a client doesn't have faith in your ability to deliver, to a position where the client does.
Your clients trust you implicitly, or they wouldn't have chosen to do business with you in the first place. There aren't degrees of trust, at least not between business entities. Either clients trust you, or they do not, or they don't have enough information available by which to make a decision. If they do trust you, the only thing that will keep them trusting - and keep them as your customers - is repeated on-time and on-budget delivery of a satisfactory product or service. The easiest way to compromise that trust is by, of course, providing something less than what your clients have become accustomed to. On the other hand, you can compromise this trust by attempting to mutate your professional relationship into something more personal.
Some people like to argue that it's best to treat clients "in the way you'd like to be treated - like family," as if the phrases on either side of that dash were somehow synonymous. From at least one reasoned perspective, there isn't a more dangerous way in which to conduct business. For the most part, your clients could not be less interested in the details of your life. Nor do you need to share with them your dreams and aspirations. Doing so is an act of brazen selfishness, and the very inverse of the axiom that the customer ought to be your focus.
However, saying that the customer comes first doesn't mean that you should switch chairs and take an interest in your client's personal life, either. In many respects, that's even worse. Whether you're sincere, or just faking it, trying to get intimate with your clients is a gross violation of privacy. Not only that, but if your primary objective is to maintain trust, getting personal is an awkward and circuitous way of going about it.
Socializing with clients is unavoidable. Taking an established client to dinner or drinks transforms your contract, whether written or unwritten, into something beyond business.
Maybe your intentions are explicit, or at least clear, and having a personal relationship with the client is more important to you than making money could be. There's nothing wrong with that, in and of itself, as long as you understand that any fruitful personal relationship could hamper the business one. However, if that's not the case, save yourself the trouble and keep things nice and clean.
The Brits have the right idea here. As befits a boisterous American, I once referred to a new English client by her first name. It's a mistake I came to regret, and it's not as if she was significantly older than me, as she was some gray-haired grande dame in pearls and a sensible hat. To New World sensibilities, she certainly wasn't old enough to have warranted the honorific "Mrs." By using her first name I'd implied a degree of familiarity that I hadn't earned and never would. If that wasn't clear at the time, it became unmistakable one second later when she called me "Mr. McFarlane."
The following advice might contradict every book on sales ever written, but no, your customers are not buying you. They aren't even necessarily buying your product. They're buying what your product can do for them. Ultimately, they're spending money in exchange for a marginally easier or more efficient life. There's an advertising axiom that illustrates the point succinctly: "People don't want a bar of soap. They want clean hands." Nor do they want a soap salesman, no matter how friendly and engaging he or she might be.
The Bottom Line
Professionalism means keeping a professional distance. As someone who deals largely in digital products and services that don't require anyone to kick the tires before buying, it's easy to keep my business relationships purely commercial. You may take ownership of what I'm selling, along with this invoice, and in return you can drop money in my bank account. Everybody wins. Most of my clients live far enough that I don't see them, and even my local clients have little use or need for face-to-face contact. They have families and friends of their own and don't need to devote more of their precious time to me.