Your ding on your score has to do with a few things. First of all it is a credit inquiry, having those will lower your score. Second, New accounts lower your account age average. Lastly If you carry a balance it could lower your score due to Credit Utilization. So to say it will come right back on a set time frame is hard to say. After I have opened accounts it has taken between 6 months to a year to come all the way back! My credit history is long so a new card doesn't afftect my credit age much. If you are new to credit then a new cc could cut your age in half. 

My opinion  around 6 months you should start to see the increase again.

Hope that helps!

Good Luck

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Starting Score: 719
Current Score: 809
Goal Score: 825

Take the FICO Fitness Challenge

+1  Typically you will see an initial ding, however it's necessary to develop new positive TLs that will allow your scores to grow.

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Starting Score: 504

Current Score: EQ FICO 819, TU08 775, EX "Who Knows?" Quizzle 756
Goal Score: All Scores 760+, Newest goal 800+
Take the myFICO Fitness Challenge

FWIW, I applied for 2 cards last July 30 and added some additional debt as well as lowered by utilization %.  My Equifax score went from 800 to 761.  It was only last week that my score started to come back up and even then it was 1 measly point.    I expect it will take most of the year to bounce back.

___$13.5k______$20k_______$20k_______$25k_______$20k____
Starting Score: 676 Feb 2008; Current Score: 756 May 2013; Goal Score: above 780 this year
Oldest Account: 31.1 years; Current AAoA: 14.6 years; Current Utilization: 5.2%