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There is a link between bond basis and money market basis. In particular, we can see that:

R(B) = R (M) * (365/360)

R(M) = R(B)* (360/365)

Where:

R(B) = interest rate on bond basis

R(M)= interest rate on money market basis

Why?

Money market basis yields roughly 1.389 (=365/360-1) more interest than bond basis for the same nominal interest rate. In other words, to generate the same amount of interest, R(B) should be proportionately higher