Mann,
Many solutions exist for the problem you've posed.
However, before jumping right in to the solutions let me first mention that many creeks fall under the Department of Natural Resources and Army Corp of Engineers regulations. In short, you, or the agency you represent, could be responsible to the abovementioned agencies for a "No-Rise" condition. This condition stipulates that an obstruction placed in the waterway will not cause more than 12 inch rise in the water level upstream of the bridge for a 100 yr event.
Now, on to the alternatives for construction. Many assumptions have to be made such as whether this is a girder bridge or a slab bridge. Many concrete slab bridges were designed in this span range as were non-composite steel girders and slab bridges. Alternate One. Since the stucture is short (about 27 feet)it is possible to remove the deck (it's probably old and deteriorated anyway)and drive piling, place pile cap and substructure concrete and then place a new deck on the structure. Traffic during the construction phase is rerouted adjacent to the bridge. Perhaps on some large CMP and gravel, which of course all needs to come out at the end of the project. Alternate Two. If the slab absolutely must stay on, smaller piles (like pin piles or micro-piles can be driven with little headroom and the remaining substructure constructed afterward. The slab can be lifted (oh, so slightly) and set to bear snug on the newly constructed substructure. Naturally, this assumes that the deck has adequate top reinforcing to sustain tension from the negative moment introduced at the support. If not, then we're back to replacing the deck (see alternate one). Alternate Three. Since the structure very likely is 27 feet long and has vertical abutment walls at or about the 27 feet range (open span) then why not proposed a triple box culvert (triple cell culvert) these are used by many states as a standard in this situation. With 3-10' cells you've got 30+ feet of span. Alternative Four. Replace it with a precast CONSPAN culvert or equivalent. The precast alternatives are usually constructed in days rather than weeks.
In short, its going to cost a lot to perform the necessary foundation work within those constraints. More than perhaps some other alternatives. Unless rock is close to the surface, you're going to need a deep foundation to prevent undermining of the interior bent foundation. Driving pile can be detrimental to the existing abutment foundation. Whether or not they are founded on pile. Explore your alternatives!