The number of devices and internet traffic for applications connected to the internet increases continuously. Devices provide increasing support for multi-homing and can utilize different access networks for end-to-end communication. The simultaneous use of multiple access networks can increase end-to-end performance by aggregating capacities from multiple disjoint networks by exploiting multipath communication. However, at this current point in time, multipath compatible transport layer protocols or multipath support at lower layers of the network stack have not seen widespread adaptation. Tunneled transport layer access bundling is an approach that allows for all types of single-path resources to exploit multipath communication by tunneling data over a Virtual Private Network (VPN) with transparent entry points on the User Equipment (UE) and on the internet. Commonly, such adaptation utilizes a single queue to buffer incoming packets which pose problems with fair multiplexing between concurrent application flows while being susceptible to bufferbloat. We designed and implemented extensions to Pluganized QUIC (PQUIC) which enables Flow Queuing Controlled Delay (FQ-CoDel) as a queueing discipline in tunneled transport layer access bundling to investigate if it is possible to achieve fair multiplexing between application flows while mitigating bufferbloat at the transport layer. An evaluation in the network emulator, mininet, shows that FQ-CoDel can add mechanisms for an instant, constant, and fair access to the VPN while significantly lowering the end-to-end latency for tunneled application flows. Furthermore, the results indicate that packet schedulers, such as Lowest-RTT-First (LowRTT) that adapt to current network characteristics, upholds the performance over heterogeneous networks while keeping the benefits of FQ-CoDel.