Let p > 1 and let ρ be a non-negative function defined in R +. A function f ∈ H(D) belongs to the space B p (ρ) (see [4]) if f p Bp(ρ) = | f (0)| p + D (1 − |z| 2) f (z) p ρ 1 − |z| 2 (1 − |z| 2) 2 dA(z) < ∞. In this paper, motivated by the works of Békollé and Bao and G ¨ o ˘ g ¨ us, under some conditions on the weight function ρ, we investigate the closures C B (B ∩ B p (ρ)) of the spaces B ∩ B p (ρ) in the Bloch space. Moreover we prove that interpolating Blaschke products in C B (B ∩ B p (ρ)) are multipliers of B p (ρ) ∩ BMOA