I can be found as Sols_Light on PSN and I know exactly what you mean about Bone Head. That fight is a real wall you come against at the point you reach it, because it's much tougher than the vast majority of quests. Even if you go do all the other quests first (I highly, highly recommend this), you're going to find Bone Head tough.
What can you do?
Find Pink boxes in places you can access without too much pain and go open them repeatedly. Pink boxes contain the best weapons you're likely to find and finding something which fits your character well would be a big help. Keep a special eye out for elemental attacks when you're comparing weapons, I consider one damage on an elemental weapon to be worth two on a normal weapon. All the elements except shock are incredibly useful on nearly everything. Shock comes into its own with the endgame bad guys who are mostly shields. Fire and Corrosion do damage over time which stacks the more you get onto things. Corrosion also does more damage the more of it you use, so it seems to start with less damage over time than Fire and builds up. Blast is basically extra kaboom on hit and there's very few things immune to it.
There's various ways to play each character type. Solo, I've had the most success with a Soldier with the Ammo Regen abilities and a side focus on Shotguns and a bit of extra damage from my turret. The luxury of never having to worry about ammo is just wonderful and the shield the turret gives is really good for keeping enemies away. Shotguns have taught me the importance of accuracy and the use of scopes. I know it's counter-intutive but a Shotgun with a good accuracy and a scope can produce some very surprising results due to the power of Shotgun blasts.
My Sniper is definitely a sniper. I've learned from this character to keep a corrosive Sniper Rifle on hand for every character as you can take down stationary gun emplacements with easeusing one. These are often quite difficult to deal with Solo without a vehicle. Other than that, Snipers are very useful for teaching you the power of the Headshot and that reload times on powerful weapons can really be important.
My Brick is all about enhancing Blast weapons and going into the Melee Rage mode when something's too much. I don't like Launchers, I can't get Criticals with them easily enough so I tend to play my Brick a bit more like a very beefy Soldier who's not so fussy about guns and really likes explosive ones.
My Siren loves her fast weapons and has taught most of my other characters to do the same. Fast firing weapons like SMGs are amazing when combined with Elemental damage, try it and see. Again, this can work for pretty much every character, the Siren just has some extra powers to increase fire rate and elemental damage to push the envelope.
There's plenty of other playstyles and you can mix and match whatever I've said above into pretty much every character. I'd recommend focussing on a weapon type if you have the ability to get more damage out of it, but keep some other types on hand. One Slow thing with stopping power like a Shotgun or Revolver; one fast, preferably elemental weapon like a SMG, Assault Rifle or Repeater Pistol; one Long Range Killer like a Sniper Rifle or Rocket Launcher and then other favourite weapons to keep elements or other things you like on hand.
Look out for a healing shield and buy one as soon as you can, nothing else compares to one. Keep it upgraded with the highest shield you can find with health regen and if you get faster health regen, that's a bonus. Keep an eye out for Transfusion grenade mods too. Being able to not only damage enemies behind cover but steal health off them is a literal life-saver, especially in Solo when there's no one else to save you.
Remember to use your specials and enhance them for the things you feel you want most, you can always change talents later.
