Who greets first
يُسَلِّمُ الرَّاكِبُ عَلَى الْمَاشِي، وَالْمَاشِي عَلَى الْقَاعِدِ، وَالْقَلِيلُ عَلَى الْكَثِيرِ
Yusallimu-r-rakibu 'ala-l-mashi, wa-l-mashi 'ala-l-qa'id, wa-l-qalilu 'ala-l-kathir.
"The one riding greets the one walking, the one walking greets the one sitting, and the smaller group greets the larger group."
Narrated by Abu Hurayrah. Sahih al-Bukhari 6232, Sahih Muslim 2160
A short reflection
Salam has a direction, and it usually runs from the one who has more ease toward the one who has less. Do not wait to be greeted.