Hehe this sort of reminds me of myself c:
I'm not very good at making new friends and i went to secondary school/high school this september and all my friends split including my best friend so shes got her own single best friend thing now.
So i had to try to find my own as well. When i first started, the few weeks were hard because nearly everyone in my tutor (class) knew each other already and most of them had their best friends by their side.
Then i noticed this girl i will call her L, she wasn't so happy even with her best friend there with her. So with all my confidence i said ''are you okay?'' and i tried to reply with : ''Hi my name's____'' We became friends =)!
and like you i couldn't think of anything AT ALL to talk to her about. I tried to tell her about things in my past and what i enjoy and somehow she managed to go along with my awkwardness .. and xD i don't find it strange if you asked me what did i do this weekend but it would be pretty boring in the end.. You'll know the right best friend soon
A person who you can never pause with conversations with. I'm still trying to make my friendship with L into a close friendship and yes i have boring talks with her, it happens xD If you go silent just laugh. I always do.
Sorry if this doesn't help or make sense xD I literally just typed this through my mind.