Change your hotel!
Transport is a major issue in Istanbul. The last time I went there on a work trip road travel from the airport to an office on the same bank of the Bosphorous took 3 hours. This was an exception but it is always pretty bad. The Asian side is a cheaper place to stay and the airport zone is not great anyway.
Until the tunnel is complete across the river (2014) there is also no rapid public transport link and the queue for the bridges in peak hours is significant.
Here is a map of the cities public transport network, print before you go as I didn't find one as good elsewhere.
You can see the disconnect that the river imposes. This is set to continue in the future too as one of the bridges needs long term maintenance that is set to require its closure and the city continues to grow rapidly.
Having said that there are some great examples of public transport in the city, the locals don't seem keen but the Metrobus is an example of what can be done with buses and should be extended in an exclusive lane across the Bosphorus, it would move more people than the current traffic jam.
As someone else said an option may be to travel from the airport to the Golden Horn and get a ferry across but it really is quite a long way and you are going to be a sweaty mess by the time you get to work!
Oh I should also mention that the taxi experience is rarely great, out of eight taxi rides I got only one successfully took me to the right place despite written addresses. One of the taxi rides ended rather unpleasantly with a row as the driver tried to rip me off royally.
Enjoy your trip it is a interesting energetic place.