I am not sure if this would qualify as a workaround for what you want to do but this works.

tt = Table[BesselJZero[0, i] // N, {i, 25}]

FindRoot[BesselJ[0, x], {x, # - 1, # + 1}] & /@ tt

I am not sure if this would qualify as a workaround for what you want to do but this works.

tt = Table[BesselJZero[0, i] // N, {i, 25}]

rr=FindRoot[BesselJ[0, x], {x, # - 1, # + 1}] & /@ tt

Show[Plot[BesselJ[0, x], {x, 0, 100}], 
 Graphics[ Point /@ ({x, 0} /. rr)]]