Conversation with a girl in university

Conversation with a girl in university Yesterday i saw a girl sitting, and i asked here if i can set next to her, she said yeah its fine sit. i sat down and starting doing my things. After like 10 min i saw her reading a book and i wanted to start with her a conversation, i felt anxiety thinking how i start with her and i felt that i will stutter in some words, but i pushed myself and i talked, i start talkin with her normally and she smiling when she, but i stuttered in some words and that words i thought about them before that i will stutter, i felt anxious and embarassed after that but we kept talking normaly. Finally i said to her bye and good luck and she smile and respond to me with the same, but i felt so anxious and embarased when i can't pronounce the word normally