I have a Zastava in 375H&H imp that I just bought, the rifle was in a ramline stock. Have found a beech stock and getting it bedded - steel bed I think.

Should it be crossbolted before I fire it or could I put a few rounds through it first, does it even need to be crossbolted?

properly glass (or steel) bedded the crossbolts aren't needed but they are reasonably cheap and easy to install and look great so I'd put them in anyway. They sure can't hurt anything but again.....a lot of 375 H&H rifles work fine with out them.