In a SVD with user/video bias, why is the UV contribute so small?
I think that depends on the pattern of your data, its skewness and sparsity. 
Because it would press these two bias term, which is designed to detect the difference with global mean. 

For example, you can plot mean and std of the user's bias: ($R_u$ - global_mean) then make a histogram of std. Another way, just make up a rating matrix $R'$ according to the $\mu + B_u + B_v$ you've got. And run the solver again and see what happens. These parts play its own role, even your change on global_mean would make a difference to the final RMSE, I think the role of that latent factors are born to capture the REST non-linear pattern in user &amp; item's interaction.

So, as for your question:


  Why does this part contributes so small?


Again, you can simply using $R = UV^T$, in this time, I think it contributes quite a lot, right? The contribution of each part is hard to say.