Yes, there is a way for them to test it. But honestly, IMO if they're not pushing for it, I'd try to just stay put. Once you walk into the hospital with your water broken they'll likely put you on (an arbitrary) clock to deliver. If your water is broken contractions will likely start in the near future. Just take precautions to keep things clean JIC that is the situation (change your pad frequently, nothing inserted into your vagina, be diligent about wiping/cleaning the area, etc.).
And yes, sometimes it does start as just a trickle, but also keep in mind only about 10% of women have their water break before labor starts and it could also be some sort of discharge. I''d just stay put for now and see what happens!
ETA: Just realized you're only 35 weeks. Hmm... hopefully contractions won't start then :) If you're really worried that it is amniotic fluid yes, they can test it, and you definitely have the right to have them test it for your peace of mind. If that's what you really want call them back and ask what you need to do to get it tested (i.e. should you see them or head to L&D). I'd probably still just wait and see for a little bit to see if you observe more fluid. At this point it's unlikely that baby is sitting low enough to block the fluid from coming out, but there is always a chance it's just a slow leak further up that could cause more of a trickle.