Sadly, the Timonium station hasn't seen railroad passenger trains since 1957 (that is "steam" railroad passenger trains. Light rail trains still serve the Timonium area, but I am unsure where the original PRR station was.
The closest Amtrak station is Pennsylvania Station in Baltimore. If you don't have too many bags, I suggest taking the light rail out of Penn Station to Mt. Royal Ave/University of Baltimore station (you can see architect E. Francis Baldwin's 1896 Mt. Royal Station close-by), then catching a northbound train (on the platform closest to the parking lot) marked "Hunt Valley", and ride up to Timonium Fairgrounds station, right around the corner from the hotel. Soon there will be a number published to call for someone to pick you up.
If you do ride the light rail north, you'll be riding on the former PRR/PC/CR Northern Central Branch, one of the oldest mainline railroad right-of-ways in the country, just a few months older than the more famous B&O. If you look carefully, remains of industrial sidings can be seen, many served by the PC at least in it's early days.
When the light rail train leaves Mt. Royal/UB station, it will curve sharply to the left crossing over an intricate interlocking, plunge under the Howard St. bridge (with only a few inches clearance) then climb a hill to cross over CSX's Philadelphia Sub (Baltimore Belt Line). The light rail will then decend and curve right, following the edge of the CSX R-O-W. A tunnel is just ahead, under North Ave. These tunnels where used by the Pennsy and PC to reach Bolton Yard, where the UB parking lot is now. After the Light Rail's North Ave. station, the line is on former PRR/PC right of way.
Boy, ask for the time of day and get the history of the clock....