Read as 'tsuwamono' it's a classical warrior. Read as 'hei' it's an army private.

What a Japanese person actually thinks
Most readers default to the plain military sense — the character in 兵隊 (troops) and on a shogi piece. The poetic classical reading is available but not the first thing anyone reaches for.

Meaning

Literally: soldier; arms
Actually: Depends entirely on the reading, and a tattoo can't specify one. 兵 is the ordinary word for soldier or troops; the classical reading tsuwamono means a great warrior.

Scores

Naturalness●●●●●

Real character, ambiguous alone.

Coolness●●●●●

Clean and dense. It just won't reliably land on the meaning you want.

Watch out

mediumAlso a shogi piece (歩兵). Some readers will see the board game before the battlefield.

Get this instead

武 bu
the martial; martial virtue

One character covering the whole martial concept, with no rank attached and no ambiguity.
武士道 bushidō
the warrior's code

If what you want is the warrior as an ethical figure rather than a soldier.

On skin

兵

Orientation: either

Brush.