Bridges and membranes are supposed to keep solutions separated while keeping ion conductivity. It is usually trade-off between both conditions.

Does filter paper keep solutions separated?  I do not think so. Difference of pressures or levels would cause flow to the other side.

Somewhat better would be soaked thick paper for drawing/water colour painting. Or even better cardboards  But consider long term desintegrating effects.

Try some ceramics, like porous flower pots(?), long term soaked in some suitable inert salt solution.

Or (not too porous) fritted glass as @Ed V has mentioned.