Spoiler: I don't take photos “Behind the bushes and following clients.” I think you know this situation: you booked a photographer, you are going to a special spot, start proposing and at the same time a photographer appears from the bushes and starts taking photos or maybe not!
Yes, this option has a place to be and if you like it, just find a photographer who can help you. 

Why I don't take photos “Behind the bushes”? 

I’ve had bad experiences with this way!
•  Once tourists stood in front of my camera (I think they wanted to record this moment too and they didn't see me), so I took not good photos, I lost some moments. 
•  Proposals are always nervous events and I'm nervous too. When I can't control a lot of moments such as sudden people in front of my camera, I get nervous and may make mistakes.
•  We don't know each other. And yes, we can share our photos to recognize each other, by the way, sometimes you are so nervous and you can't find your clients or your photographer. Or one of you is late. 
•  Once, my clients have gone to the wrong place and I was running to them! I almost lost these moments. It wasn't my mistake but my work is great photos, and if you lose moment, you lose a moment! 
•  And the most main thing: when you book a photoshoot as a regular couple photoshoot both of you will prepare for that (clothes, make-up, your mood). When you go for a walk and then it will happen, your partner is dressed as usual in most cases, but this is still a special moment. But if you ask your partner to dress up I think it's suspicious! You will lose the effect of surprise and the most sincere emotions.

However, I have the best alternative options for you!
This is my opinion and my experience as a photographer.
Keep reading!