This question is written so as to suggest that yes, the poetic speaker does really seek rest in this poem, "The Vagabond." The word in the first stanza that might indicate this interpretation is "Bed," the phrase is "Bed in the bush," and the verse (i.e., line) is "Bed in the bush with the stars to see." Unfortunately, if you embrace this reading, that the poet really seeks rest in the poem, you disregard the majority of the first stanza and contradict the second stanza, and you can't adequately support this thesis of seeking rest with other textual evidence. It's good to note that the second is also repeated as a refrain in the last stanza closing the poem: this repetition marks its importance.
The second stanza, the refrain of the fourth stanza, means, by way of paraphrase: Let the storm (blow: storm, strong blast) fall upon me either soon or later; let what will be in the sky be. Give me the ground of earth and an open road before me. I do not seek wealth; nor do I seek hope or love; nor a friend who knows me. All I want is the heaven above and a road to walk before me.
Interestingly, Robert Louis Stevenson made a practice of taking walking tours through England and especially through Scotland. One of his best short stories, "The Pavilion on the Links," occurs while the hero is on a walking tour in Scotland. The second stanza of "The Vagabond" reflects this walkers' spirit--it could possibly be said to reflect Stevenson's personal experience as a walker, thereby making the poetic speaker's voice synonymous with the poet's own voice--and contradicts any notion of the vagabond wanting rest. This is particularly important to note because the stanza is twice written in the poem.
The actual meaning of the first stanza, based on the words Stevenson chose, is this, by way of paraphrase: Let the waters flow past me (lave: waters as in a river flowing). Give me the jolly sky above me and an open road near me. My bed will be in the bush with the stars to see as my ceiling; my bread I will dip in the river [instead of in a sauce or in coffee]--There is the life for a man with my likes; there is the life for me forever.
While bed is mentioned and bed does associate with rest and wanting rest, it is countered by the activity of the lave (flowing water), the byway (open road to walk), and breakfasting with flowing water. The last lines declare that the life described is the life the speaker wants. But what life is described? Rest is alluded to once. Activity is alluded to three times. Activity overpowers rest: therefore the life described that he wants is the active life with rest only at night under a star-studded ceiling. Therefore, the poet really seeks activity in the poem "The Vagabond."