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In this paper, we investigate some properties and identities for fully degenerate Bernoulli polynomials in connection with degenerate Bernstein polynomials by means of bosonic <i>p</i>-adic integrals on <inline-formula> <math display="inline"> <semantics> <msub> <mi mathvariant="double-struck">Z</mi> <mi>p</mi> </msub> </semantics> </math> </inline-formula> and generating functions. Furthermore, we study two variable degenerate Bernstein polynomials and the degenerate Bernstein operators.