AD is just terrible on her. Compare her to say.. Xin or Yi some other autoattacker. you can see that AD Elise is subpar compared to AD Sion, Xin, Yi, Fiora, etc.
She is squishier than a normal melee AD.
Her AS per level and base AS are weaker than melee AD.
She has NO SCALING SKILLS whatsoever with AD.
Her AS steroid is only 3 seconds. Its strong but on average less useful than say Xin's 80% for 6sec.
She only has that 1 steroid. Xin has AD steroid, Sion has AD and AS and lifesteal, Yi has AS, AD.
She has spiderlings which dont scale on AD and apply minor damage. She has a great gapcloser, but has NO SLOW. This really kills her as a melee since she needs Rylais or Mallet to be able to chase worth a ****. Maybe furor enchantment or ghostblade.
Tanky AP works a lot better. Her ratios arent great but she has a LOT of them!
Q has two buffed ratios, roughly equivalent to 0.6 AP ratio vs a foe @2k health.
She has 0.3 AP ratio which cost-wise is about equal to 0.55 AD as onhit damage.
Spiderlings have 0.2 AP ratio. With 5 of them thats significant.
She gains extta health with W up based on AP.
Her W spiderboom is 0.8 AP ratio.
Thats a lot of stuff. She has decent enough burst, though relies on melee to deal extra damage. But with a 3 sec steroid she isnt meant to duke it out in melee for extended duration.
Remember, you DONT have to rush tons of AP. Best bet is lots of magic penetration (sorc shoes, guise, abyssal), and some decent tankiness (frozen fist, rylais/Rod/etc).
That lets her due near true damage to many foes, ahve a good burst, penetrate her onhit damage, plus give her good armor/MR/ghealth.