There are many other guides on how to play the hero so this is simply my proposal of items and their justifications for hard-carry Bristleback as I couldn't find one already on here.
With the new changes to Warpath Bristleback is now more viable than ever for the hard-carry role. At level 25 with just a Daedulus and 210 bonus damage from Warpath Bristleback has 420 damage, a crit on that would be 1008.
With these items your late game damage will be on par with Slardar, Lifestealer and even Faceless Void, not to mention that you come on-line faster.
Ring of Basilius gives Bristleback much needed mana regeneration and armour for the early game.
Power Treads give much attack speed and strength + the added possibility of switching to int to make the most of Bristleback's low starting mana pool.
Medallion of Courage gives you heaps of early game damage synergising with Viscous Nasal Goo and even more mana regen to work with (More on this in Damage)
Vanguard can be skipped for Armlet of Mordiggian. The active of Armlet of Mordiggian gives 475hp, 225 more than Vanguard. It also gives +56 damage (including the strength gain) and +15 attack speed. Armlet of Mordiggian gives 7hp regeneration; 1 more than Vanguard while also granting 5 armour. Perfectly toggling Armlet of Mordiggian is infinitely more useful than the damage block Vanguard gives in a sticky situation and Armlet of Mordiggian does not fall off after the early game.
To counteract the hp loss pick up a Morbid Mask which will be built into Vladmir's Offering, Mask of Madness or Helm of the Dominator.
Vladmir's Offering gives +15% damage on you and your teams base damage and from attributes. It provides your whole team with +5 armour and stacks with the aura from Assault Cuirass. This is the only lifesteal option that works with Desolator.
Mask of Madness gives Bristleback 100 attack speed and +30% move speed to chase and make use of the insane damage from Warpath. It also gives him the sustain which he is missing out on from the forgone Vanguard. Don't turn it on when you are getting chased down because it will only hurt you. However the bonus 30% damage your enemy gets means more Quill Sprays, and with the huge amount of damage you have, if you are attacking you will be able to keep yourself alive through lifesteal.
Helm of the Dominator has the added potential of getting the Packleader's Aura from the Alpha wolf. You can stack ancients and kill them off with the physical damage from Quill Spray and also have the possibility of building it into a Satanic later on.
After this you can pickup a Vitality Booster and work your way to Heart of Tarrasque.
After this you can choose your DPS items, picking a mix between Daedalus, Skull Basher, Maelstrom and Desolator. Note that Skull Basher and Daedalus synergise well with the attack speed from Mask of Madness. Also, Desolator does not work with Mask of Madness or Helm of the Dominator but you can always pick up a Medallion of Courage instead.
Skull Basher is very useful when chasing and 1v1 fighting and builds into Abyssal Blade giving you +100 damage as well as the the very useful active Overwhelm stunning your enemy for 2 seconds.
Desolator synergies well with Viscous Nasal Goo reducing the targets armour by a further 7, giving a total of -16 armour reduction amplifying the damage of both your right-clicks and Quill Spray(physical damage) by a whopping +49%. Add Medallion of Courage and ***ualt Cuirass onto this and we are up to -27 armour capping out at +60% amplification. This is Amplify Damage levels of armour reduction.
Maelstrom is a great farming item and builds into Mjollnir which will give you great attack speed and its very dangerous active Static Charge. Having this on while enemies try to chase you down to add to Quill Spray is a recipe for a RAMPAGE
Assault Cuirass should be picked up to maximise your EHP from Heart of Tarrasque. However, forgoing this means you lose HP faster, meaning more Quill Sprays and therefore more stacks and more damage, especially when your Mask of Madness is activated. Buying another Heart of Tarrasque afterwards could prove more useful in the right situation. Say you have 4000hp (level 25 with 2 hearts) with Mask of Madness activated. While taking the bonus damage you have an EHP of 2800 not taking into account your current armour. 4000/8=16 Quill Sprays. Thats 80+110+140+170+200*12=2900 physical AOE damage. That is effectively a Blade Mail which goes through Magic Immunity. You will only release a Quill Spray when you take damage from behind however. You can run in out of combat like this confusing your enemies as to who is running from who before you turn around around and smash them into the ground.
Black King Bar is absolutely necessary certain lineups as you are facing the enemy to do your damage.
Radiance will increase your "running away power" greatly, but is lacking in the right-click department for its cost.
Monkey King Bar with great attack speed means you can constantly mini-bash your targets and has the added benefit of True Strike against Phantom Assassin, Riki, Brewmaster, Troll Warlord and Talisman of Evasion. With +88 damage and 35% to deal a bonus 100 damage this bolsters you DPS considerably.
Finally we have Divine Rapier giving you +300 damage which must never be ignored, even though it has its risks.
Bristleback can forgo items like Drum of Endurance, Phase Boots and Sange and Yasha because of the great move speed he gets from his ultimate Warpath (not to mention the damage) and the slow from Viscous Nasal Goo. He can skip farming items like Hand of Midas and Battle Fury because of his ability to farm heroes rather than creeps. With a free +210 damage(only 90 less than Rapier) and -8 armour debuf(more than Desolator) he comes online faster than Lifestealer and Faceless Void and with the right itemisation can give them both a right proper bashing.