That's what it all comes down to in the end..
You need to put a value on how much you are willing to spend on a FA. Let's say you are willing to go as high as $8m a year on Jeremy Numbnuts as your new RF. So you have to decide . . . (a) do I just put a pre-emptive maximum bid of $8m a year on Jimmy and if I win him, great, but if somebody outbids me, then so be it; or (b) do I try to get away with lower, incremental bidding and hope to sign him for, say, $5.5m a season and run the risk of sombody signing him for $6m a season at the last minute.
It all comes down to setting a limit for yourself, then deciding your strategy.