Manipulating Deformable Linear Objects (DLOs) is challenging in robotics due to their infinite-dimensional configuration space and complex nonlinear dynamics. In teleoperation, depth uncertainty hinders state perception and reaction. AssistDLO addresses this challenge as an assistive teleoperation framework for DLO manipulation that combines real-time multi-view state estimation, visual assistance (VA), and a geometry-aware shared-autonomy controller based on Control Barrier Functions (SA-CBF). While traditional shared autonomy methods often rely on simple geometric attractors and may fail to preserve DLO geometry, SA-CBF acts as a geometry-aware funnel, facilitating precise grasping while preserving the operator's high-level authority. The framework is evaluated in a bimanual knot-untangling user study (N = 22) using ropes with varying length and rigidity. Results show that the effectiveness of the assistance depends strongly on operator expertise and DLO properties. SA-CBF provides the strongest gains for naive users, acting as a skill equalizer that increases task success from 71% to 88%, and is effective for stiffer ropes. Conversely, expert users prefer VA, and highly compliant, long ropes benefit more from visual support than localized action assistance. Ultimately, these findings demonstrate that effective DLO teleoperation cannot rely on a fixed strategy, highlighting the critical need for adaptive, user-aware, and material-aware shared autonomy.