To say anything of the Sikh Gurus taking any inspiration from Bhakti movement is fallacious. Sikh Gurus included the writings of other saints in the Guru Granth Sahib; implying that as taking inspiration from them is false.

From Parasaraprasna, Kapur Singh, Guru Nanak Dev University Press, Amritsar

 Thus those who see in the origin and contents of the Sikh
movement anything of this VaiSlJavism or the historical Bhakti
movement of the Middle ages, which was based on this VaiSDavism
or cognate propositions, show a complete lack of understanding ofthe
real nature of Sikhism. Beyond the fact that Sikhism is of historical
proximity to this Bhakti movement of the Middle ages, and that it
somewhat partakes of the atmosphere and temper of VaiSDavist
climate, it has not much in common with the latter. Among the
principal features of this climate are its anti-Brahmanical attitude, its
preference for vernaculars26 over Sanskrit, its total surrender theory,
such as Lokacarya's marjara27 doctrine, its stress on devotion through
image-worship rather than through knowledge, and its own peculiar
forms of ritualism, such as caste-marks.

It is easy to demonstrate that similarities of Sikhism with some of
these features are not so intimate or fundamental as to suggest any
direct or indirect borrowing.