First, what scope are you using? This is a key part to how easy or hard it is to zero a rifle. Typically, cheap scopes don't track true or at the exact distances labeled. It can make it a very difficult job to accomplish without spending a good deal of money. That's not to say all cheap scopes can't be zeroed easily or that all expensive scopes track well, just a generalization. If you look at the cost of ammo, spending $300-$400 on a scope quickly becomes justifiable if you spend a few hundred rounds with a wandering zero.
Assuming the scope works as advertised, I would definitely laser bore sight first. Bolt rifles, as many have said, are simple enough to just pull the bolt and look down the bore. Here though, it's a bit more difficult and using a bore sighter is necessary. Another option is to buy a sheet or two of poster board and tape them together. Aim at the middle, see where it hits, and go from there. If you have no holes on the board after the first shot, aim at the lower edge. At 25 yards, you shouldn't be off more than a poster board if you have the scope centered and everything mounted correctly. If you do miss the board, I can typically see dirt fly if I'm shooting low. With two poster boards taped side by side, I haven't seen a case where I missed left/right when aiming at the center. So if there is no dirt flying and it misses, I tend to then aim at the bottom edge of the board as I am guessing it's going high. I keep working down until I see impact on the board/dirt and go from there.
To get within an inch or two of your absolute zero, with an accurate scope, it shouldn't take more than 10 rounds or so. If you want to get exactly centered it can take quite a few more rounds, but a hunting accurate zero really shouldn't be taking 100 rounds. I would also try to find a friend to go with you. It makes spotting a bit easier and it also lets you switch shooters if things start going bad.
