If it's just started making a noise and it's not ridiculously noisy then it will almost certainly cover 300 miles with no problem (but I offer no guarantee!).
It takes only a minuscule chip on a ball or a race to make a surprising amount of noise, but provided there is grease in the bearing they will usually go for thousands of miles like this.
My civic (same as Gaijins) also had a slightly noisy rear bearing (common problem with them) and I did over 5000 miles before replacing it, even though it hadn't actually become any worse during that period.