I'm not a hundred percent sure what you're referring to when you say 'conversation based RP'. My immediate thought is short, first-person perspective (using me and I) replies that go back and forth in a similar way to how a conversation would. Either writing in properly punctuated sentences or with actions in *asterisks*.
EX. Punctuated Sentences; Breathing heavy I locked the door and backed away slowly into the living room. "Travis?" I called. "Travis are you here?"
EX. Using asterisks; *I lock the door behind me* Travis? *I start walking into the living room* Travis are you here?
In any case, this is of course far from the only style that you can RP in. Some people use the previously mentioned methods but in third-person instead, others tend to RP with a writing style that's similar to the way a novel is written, most often third person or third person omnipresent. In my experience, RPing in third-person tends to make things less personal (less you as the character more the character as their own entity) so I'm not sure if that would help you at all either? Those are the two most notable styles that I've come across but honestly, a large part of RPing is finding a style that you really enjoy and are comfortable writing in and using that.
Bottom line though, I think something that you really should consider if you're having these feelings often when you RP - especially with regards to the fact that you've stated that you worry about where the RP is going to go/what is going to happen next - is talking to your partner OOC and building communication both about the RP and about who you are as a RPer even before you start. This way you can talk through what you want to happen long before it actually does and as a result have that knowledge going into the RP. Not only is talking OOC with a partner good for developing a world/universe that you enjoy but it's also a good way to air any concerns you have and to grow your skills through mutual practice. All around good things.
Hopefully, this helps in some way or another. Feel free to tag me in a reply if you have any questions about what I've said or anything like that.
Cheers!