The route from the lower town is: Potomac Street, past The Point, up the steps to the Goodloe Byron Memorial Footbridge, across the river alongside the railroad bridge, and then down a tight spiral staircase onto the towpath. On foot it is fine and takes about ten minutes from the shuttle stop.
With a bicycle it is the whole problem. The spiral is narrow, the turns are tight, and you are carrying rather than wheeling. A light road or gravel bike is manageable by one person. A loaded touring rig, a tandem, a trailer or a child seat is not. Shuttle capacity for bikes is limited too, so do not plan on putting one on the bus.
The workaround, if you are riding rather than walking, is to reach the towpath from the Maryland side instead. There is towpath access in the Sandy Hook area downstream of the bridge and further access points at intervals along the Maryland bank. That means driving round, which feels like a defeat and saves a genuinely miserable ten minutes.
If you are walking, none of this applies. Take the stairs and stop worrying about it.