My Budew is level 13 and I'd like to evolve him before he misses any moves, but I think I am pretty far from the Happiness evaluator. Is there any way to tell if he is happy enough to evolve or should I just stop leveling him until I can get the happiness checked?
Short answer: Don't bother with Budew, Roselia can be caught on Route 7, which I'd imagine you're not too far off.
Long answer (if you insist on Budew): The Happiness Checker is in Laverre City, 6th Gym Badge, so I'd imagine you're quite a bit off. By the time you get there, Budew would have evolved purely through levels (though, in my experience, that took nearly until Lv.30). Just walking with the Pokemon builds happiness though and you could always feed it random vitamins you find as well as make it hold the Soothe Bell when you find it (forgot where).
Roselia's only useful moves within the next 15 levels are Magical Leaf (19) and Giga Drain (25) though. If you don't evolve Budew before or on Lv.25, you're stuck with Mega Drain until Lv.37 (Petal Dance).
There really isn't a great way to tell happiness outside of the Checker. Amie doesn't help in that regard either (imo, it really should have at least aided it). --- If life gives you lemons, sell 'em to Tom Nook. Black 2 FC: 0132-9980-0476, 3DS FC: 5284-2520-2972 (Pokemon IGN: Aki)