I don’t know for sure whether this will work or not, but you can try the following:
set grid noxtics noytics noztics front
From reading the documentation, it looks like this will push ticks to the top of the stack of objects when plotting (i.e., they will be displayed after the bars make them visible (I think)). Another option is to use transparency in your fillstyle, but this may not work depending on your terminal (and this may not be desirable).
source share