I think Shulk's best approach is diversity. Use both Jump and Speed for closing in. With Jump, you have crazy air control. Jump and fastfall down with N-air dives. If they're the kind that shieldgrabs air approaches, be sure you're hitting with the tip of your range. Or, cross them up, hit with the back-part of N-air as you fast fall right above their heads and behind them. And... B-air. I've had some surprising results. Jump over them, and fast fall with B-air so you hit with the end of the beam right as you land. It has great range and if they block it, it pushes them back quite a bit, abusing B-airs range and Jump's fall-speed make Shulk pretty pesky with poking at distances, and hard to punish since you have so much air control and fall with it so fast.
Oh, and try just double jumping all around the arena with Jump. Along with fast falling and faking out. It's rather funny, a lot of people get tired of my acrobatics and start getting aggressive.
Speed is pivot heaven. Pivot F-tilts are fairly safe, slashing the enemy's back as you dash and slide past them (just make sure you're not too blunt). But do it along with N-air spacing to be less predictable. N-air in Speed is also very abusable because of the shorter shorthops. Anyway, key to approaching with Speed, be annoying and make them start getting nervous. You can also try some pivot grabs as they're insanely fast and slide you a relatively safe distance on whiff, but they're especially amazing at punishing any little thing your enemy does.
Also, some people see Buster (and to a lesser extent, Smash) and go aggro trying to use it against you. So let them do that and laugh as you shut them away with N-airs and the like.
Sometimes approaching without doing anything is a good idea, since you can't be punished, you just wait for their move and mess with their minds a bit.
But in the end, the proffered situation for Shulk is making them come to you, just gotta make'em nervous first.