Colleen A.,
The only other way I know is to use the Baltimore Beltway (495). Go completely around the city - just in the opposite direction of the Key Bridge.
You can also come through town, but that would require lots more traffic and side roads.
Are you coming from the North, heading South on 95? If so, when you get to the split (495 East/South to Key Bridge; 95 South to the tunnels; or 495 West towards Pikesville/Reistertown), take the 495 West towards Pikesville/Reistertown).
This will take you a longer way (mileage) but it's all major interstate. Just follow 495; you will go past Ownings Mills, Security Blvd., Catonsville (just a few landmarks for you) and then hit 95 South again towards Washington, DC.
Let me know if you need more specifics or are coming via a different direction and I'll try to help. Ellen