I can think of a few options that may work. Some will work better than others depending how your project is set up.
The first thing that comes to mind is the Surface deformer. However, this is not for the feint of heart. It takes some getting used to. In your case it could allow you to deform the geometry onto the UV coordinates of the source geometry so it requires a meaningful UV map. You’d also need to split the source geometry to create a proxy that consists of only the polygons the deformed geometry should follow (which you can hide from the render). Some research into the Surface deformer would be advised 🙂
An alternate would be to select an edge that runs along your source geometry that roughly matches the path you’d like the glass object to deform to. Use the Mesh > Commands > Edge to Spline command to create a spline that follows the edge. Then you can use the Spline Wrap deformer to deform your glass object along that spline.
There are some details that will change depending on the look you want and how your project is set up but those two options should be good starting points.
Also for both of these methods you’ll need to make sure that the glass geometry is sufficiently subdivided so that it can deform around corners and along curves.
Darby Edelen