I used a for loop to make 4 variables:
For[i = 0, i < 4, i++,bi=0] But when I write b0 or b1 it print its as b0 or b1 not 0 or 0.
You might find it easier to do
For[i = 0, i < 4, i++,b[i]=0] b[3] (* gives 0 *) You could use ToExpression
For[i = 0, i < 4, i++, ToExpression["b" <> ToString[i] <> "=" <> ToString[i]]] and now

I am not sure why you want to do the above, there could be better ways to solve the problem you are trying to solve if you explain the purpose of doing this.
b[i_] = 0to make every value zero (as a pattern), or you could restrict it to your values withb[i_Integer /; 0 <= i < 4] = 0. Please read an introduction to the Wolfram language. $\endgroup$