Abu Tufayl reported,

I said to Ibn Abbas, "Tell me about riding between Safa and Marwa, for your people claim that it is a sunnah."He replied, "They have spoken truly and they have spoken falsely."I asked, "What do you mean by 'they have spoken truly and they have spoken falsely'?"He said, "When the Messenger of Allah ﷺ arrived in Mecca, the people came out in such numbers that even the young women emerged from their homes. No one was struck aside to clear a path for the Messenger of Allah ﷺ. So the Messenger of Allah ﷺ mounted his ride and performed the going between Safa and Marwa while riding. Had he dismounted, walking would have been more beloved to him."

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عن أبي الطفيل قال

قلت لابن عباس حدثني عن الركوب بين الصفا والمروة فإن قومك يزعمون أنها سنة فقال صدقوا وكذبوا قلت ما صدقوا وكذبوا ماذا قال قدم رسول الله ﷺ مكة فخرجوا حتى خرجت العواتق وكان رسول الله ﷺ لا يضرب عنده أحد فركب رسول الله ﷺ فطاف وهو راكب ولو نزل لكان المشي أحب إليه