The basic rule is if you can support a higher attack speed with mana, then you have increased your DPS. If you have a higher attack speed without mana support, you do the same damage in less time -- so total DPS has not improved.
But the real question is not, "Do I have more real DPS?" The question you really need to ask is, "Can my build support additional attack speed with mana?"
So a real life example of bears and attack speed on MP8.
With my current gear:
My Skorn has 1.0 base attack speed. My mana modifiers from gear include one Zuni helm with max mana and the 4 set item Zuni bonus of 20 mana per sec.
My Active mana skill modifier is Widowmaker Spiders (4 mana per spider hit).
My Passive mana skill modifier is Spiritual Attunement. (20% added to mana total, +1% regen rate).
I also use the Passive skill GF which provides burst damage and mana from health globes, but this type of mana is situational, and I do not rely on it.
My attack speed gear:
Witching Hour Belt - 9% IAS.
Theo and Tasker Gloves - 9% IAS.
Total attack speed 1.18%
Mana break point vs. Attack Speed
I also have a pair of Lacuni bracers with 9% IAS. If I equip these I have 1.27% total attack speed.
For my play style, with my current mana skills and gear, I consider the additional 9% from the Lacuni bracers to "break" my build e.g. to add too much attack speed.
Why would 9% additional attack speed "break" my build?
Because I would either have to choose another mana passive (BR or VQ) instead of GF, or I would have to throw more spiders (which in my opinion is gimping my bear damage) to make my bear attack last as long as it did before adding the additional attack speed.
How do you know for sure you are breaking your build?
Because to have life steal or life on hit you need mana. With bear builds, running out of mana is instant death on high MPs (unless you have a high rate of primary spam, or you use Rain of Toads).
So if you add attack speed items and your find yourself running out of mana (OOM) faster, or you are noticing you are dying more, more than likely you broke your build with attack speed.
So you have to either remove IAS items, or adjust your gear and/or skills to cover the higher mana usage requirement.
This is how it works for me. Your mileage may vary. --------------