In my opinion ... even though getting the test kit seems like a lot of money up front ... it will potentially save you quite a bit over throwing bleach blindly in your pool ... For example ... if you just take a little time and put your numbers into pool math - assuming your water really does come up to 48 inches (which most likely you need to measure as it will be lower than this) then adding 69 oz of 8.25% bleach will raise you from 0 to 10 chlorine ... my jugs of 8.25% bleach are 121 oz ... so adding 1 will raise it to 17 (from 0) and adding 2 jugs would raise it to 35! This could be very damaging to your liner ... and without knowing your CYA level you don't even know what slam level is.
Raising the FC in your size pool may take much less bleach than you think.