Going towards town would be easier than way from town. You could go down Streets Run Rd, then either going a hundred yards or so down Carson then climbing over the guard rail and railroad tracks to get to the Southside trail or going over the Glenwood bridge and taking 2nd Ave in to the jail trail.
There are a few other alternatives
If you want to travel during non-peak hours, I would consider taking my bike to the T.
You could ride Brownsville towards town and 18th street down the hill.
There is putatively some ghost road that goes down through the Hays wooded cliff to near the Glenwood Bridge - I don't know where it starts or what shape it's in. There might be some trails through there too.
I don't know much about this area, but I thought someone should answer.
Mick