In bi-ṭalīḥin, the preposition governs ṭalīḥ, a descriptive term referring to an implied she-camel. It can be read as the means by which the speaker puts the earlier resolve into action: his mount carries him away.
Asfār is the plural of safar, a journey. With tarakna, the journeys themselves are presented as agents that have left their marks on the animal’s body.