I want to focus my answer on maximum (im)possible bullet travel distance. This can happen to relativistic anti-bullet - heat and explosion would not have enough time to affect bullet speed and radiation will not stop it completely before total annihilation (what would happen next nanosecond is out of scope of this answer). So it is simple "total annihilation path".
Lets our bullet be anti-assault rifle bullet, i.e. 5.56×45mm NATO SS109, made of 62gr of anti-copper & mostly of anti-lead, with the bullet having a cross-sectional area of 25.5 mm^2. I do not know exact proportions, but lets say it is 10gr (0.16 moles) anti-copper and 52gr (0.25 moles) anti-lead.
This would give us 6.022e23*(0.16*29 + 0.25*82) = 6.022e23*25.4 = 15e24 anti-protons (and positrons) and 6.022e23*(0.16*34.5 + 0.25*125) = 6.022e23*36.77 = 22e24 anti-neutrons to annihilate.
Air density is 1.2 mkgr/mm^3 or 30.6 mg/m of bullet flight distance. Since both nitrogen and oxygen have (almost) equal proton/neutron ratio, we can take average air mole mass 28.98 g/mole. This would give us about 4.6e21/m = 4.6e24/km of protons, same numbers of electrons and neutrons.
So first thing we can see - anti-protons (and anti-electrons) would deplete much earlier than anti-neutrons and subsequent explosion would have two distinct zones:
- 3.3 km - path of total air annihilation. All matter would turn into gamma radiation
- +1.5 km - path of neutron-only annihilation. Air would turn into into super-heated plasma (protons+electrons+lots of gamma radiation) - a perfect conditions for good old thermonuclear reaction
Total path would be about 5 km.
So, please, do not fire bullets made from antimatter with relativistic speed in my neighborhood (i.e. Earth, or even my solar system).