Hi
I think the best thing is to choose a 'centre' as best you can by eye or with a rule, mark the centre with a dot punch and do the same on the other end.
Then mount the work between centres so that you can turn the piece, by hand, and judge if your centres are wide of the mark, mark new centres and repeat if necessary. You can move a dot punch dimple a little by using the punch at an angle.
It is not mandatory to centre drill in the lathe so you can use a drill press or even a hand drill as available. Once the centres are drilled you can remount it in the lathe and turn it true in no time at all.
If the work piece is short (more like a disc than a bar) you could mark one centre then drill through with your smallest drill to line up a centre on the other side.
Maybe you do not have a lathe dog big enough to drive it? You can wrap a strong cord around the work and anchor it to the lathe chuck but be careful of loose ends and the possibility of anything getting entangled. If your final work will have any holes in it, other than a centre hole, you could drill a hole in that position and thread the cord through or even put a bolt in the hole.
An alternative to all above would be to drill a hole through the approximate centre and mount the work on a mandrel though this would really only be practical on a short piece.
I have only a few months experience in this hobby so perhaps others will have better ideas.
cheers
John