Offered a position but only for $70K?

I'd bump that bonus ask up as well, don't want to cap yourself out of the gate. Assuming you don't get meaningful salary bump with your ask that all in comp seems low, shoot for $90/20%, and aim to land from $90-$100k all in. Key to negotiation is keeping multiple chips in the play to maximize your outcome, also be sure to include justifications/rationale. I'm not sure of your workstyle (9-5 vs go-getter), but personally I'd put more pressure on setting the bonus target higher now with an $80/20% = $96k target versus $$85/10% = $97k. Salary increases will come consistently, and are easier to argue at year end vs bonus %'s as the lion's share of the profit pool have already been allocated when you get your YE number. Much easier to argue why you didn't get your target, and worse case scenario allocate it toward bigger salary bumps if they can't justify your under performance.

I used something along the lines of this when I first went into the PE buy-side of the business and ended up getting an even larger bonus % at YE (major metro, lower cost of living than SoCal, 5+ years ago) 

"A target bonus of 20% is a reasonable ask and arguably below market. I expect to be able to hit the ground running given my experience and intend to put all my effort in progressing faster than your baseline expectations. I would much prefer the opportunity and incentive during my initial year to surpass your expectations and work toward the goal of earning that figure, if not more, instead of setting the expectation low and arguing for additional pay after the fact at year end."

Again, where you want to shake out in your final negotiation depends on your work-style & how career oriented you are, regardless I would still suggest requesting both increases (salary & bonus) to provide you the most leverage and flexibility to hit your target comp. 

Hope that helps