The addition of a small amount of polymers to turbulence drastically alters the energy transfer across different scales, and leads to the emergence of an elastic scaling range. How polymers alter the intermittency in the elastic range remains elusive. We here present an experimental study on the elastic range intermittency by probing the velocity structure functions up to the 12-th order. We show that the scaling of the longitudinal velocity structure functions exhibits a bifractal-like behavior: intermittency-free at low orders (n≤4, n being the order of velocity structure function), and monofractal with a Holder scaling h=0.53 and dimension D=2.22 at higher orders (n>4). We find that the Holder dimension is close to the fractal dimension of the the sheet-like flow structures, pointing to a connection between the elastic range intermittency and the coherent flow structures in bulk polymeric turbulence. The scaling exponents of the transverse velocity structure functions deviate from those of longitudinal velocity structure functions at high orders (n>4). This behaviour might be related to the low Reynolds number in the present study and persistent anisotropy in the flow. These results highlight the importance of sheet-like structures in polymeric turbulence and offer new insights to polymer-turbulence interaction.