I recently moved from Florida to Baltimore for work. I took two car trips, 1)find an apartment and see my job, 2)the other to officially move in. Can I deduct both trips?

No, you can only deduct #2.

This, from the IRS' Publication 521: 

Nondeductible Expenses  

You can't deduct the following items as moving expenses. 

·         Any part of the purchase price of your new home. 

·         Car tags. 

·         Driver's license. 

·         Expenses of buying or selling a home (including closing costs, mortgage fees, and points). 

·         Expenses of entering into or breaking a lease. 

·         Home improvements to help sell your home. 

·         Loss on the sale of your home. 

·         Losses from disposing of memberships in clubs. 

·         Mortgage penalties. 

·         Pre-move househunting expenses. 

·         Real estate taxes. 

·         Refitting of carpet and draperies. 

·         Return trips to your former residence. 

·         Security deposits (including any given up due to the move). 

·         Storage charges except those incurred in transit and for foreign moves