Plot hole: They have already shown that anything that comes into contact with the time bubbles is immediately affeceted. The engine running 47 days non-stop, the fruit againg, Picard's hand aging, etc. Geordi creates subspace isolation field that allows them to beam off the shuttle and onto the other ships to investigate. Problem is, the second the transporter beam hit the time bubble, it would have stopped and never materialized because it would have been affected by the extremely slow passage of time in that bubble. The warp core breach was affected as was the disruptor fire so the transport beam would have been easily affected. And they have never shown that have been able to alter the transporters in such a manner that would allow them to beam over.
Plot hole: When Picard, Geordi, and Troi encounter one of the first time disturbances it results in one of the runabout's nacelles using up all of its fuel. Data says this is due to it having been in operation for 47 days (according to the plasma conversion sensor). After this the Captain reaches for the bowl of rotting fruit which causes him to scream in pain. The other crew members rush in and Troi scans his hand. She tells Picard that his hand is metabolizing at approximately 50 times the normal rate. Data and Geordi then discover that the temporal disturbance which covers the fruit also covers the nacelle that has lost all of its fuel. Data also notes the disturbance extends outward from the hull, about 17 meters from the ship and is spherical in shape. The problem here is that according to what Data said earlier the engine was active for 47 days even though it had only very briefly come into contact with the time distortion - maybe 1 second at most, but likely far less time than this since the ship was at warp when the fuel was consumed. So if we assume the engine was in contact with the fragment for 1 second then time is actually moving at 4,060,800 times the normal rate - not 47 or 50 times normal.