If the lower crossing was to get a bus lane on both carriageways, it would allow for more door to door routes linking both sides of the Severn. @stj could upgrade his journey from car to bus! The reduction of the generic highway lanes to two in each direction would also throttle the motorists going on the crossing itself so they get jammed up harmlessly over the water out of everyone else's way rather than around Newport where they pollute the town.
"Jamming Up" traffic over the water would take much more than sticking a bus lane on the Prince of Wales Bridge. The Severn bridges are the sole part of the Cardiff<->Bristol corridor that have ample capacity - 5 lanes of it each way between roughly Magor and the English shore. Such a bus lane would have zero utility to buses as it wouldn't throttle the non-bus traffic and without toll plazas there's no routine congestion there for buses to undertake - other than straight back into a 10s of miles long queue on a Friday...
The rest of this corridor is ruined by a central core which is pretty much an engineering disaster. This is largely due to i) the Brynglas tunnels, ii) other 2 lane pinch-points and iii) that so many short hops are made by joining & leaving the M4 between the western and eastern ends of Newport via badly sited & designed junctions on bends adjacent to i) & ii). One or two of these were so bad they have been closed to useful effect, but the rest need dealing with too. Most other stretches of the corridor have been improved over the last 20 years and it would mostly be serviceable were it not for the shambles around the Brynglas tunnels.
The worst congestion occurs westbound, particularly on Fridays when it becomes a car-park between west of the Bath exit and Newport from midday until 8pm. A large proportion of this traffic is not local and has nothing to do with commuters. Bus lanes, congestion charges, Bristol council trying to ban arbitrary things in contravention of Westminster guidelines etc aren't going to have any effect on this.
The only thing worse than commuting along here by road is doing so by GWR. Trains on the Cardiff<->London route are irrelevant for the vast majority working in Bristol. Parkway is 7 miles from the city centre and of no use other than to those who work in the cluster of workplaces around the top of the M32. Temple Meads is also in the wrong place and the services from S Wales have for years been grotty, too infrequent, unreliable, appallingly overcrowded, expensive and woefully slow. Some of these have been made a little, but only a little, better recently. Woefully slow is the killer, has barely improved if at all and looks set to stay indefinitely.
Anyone commuting from the suburbs and satellites of Cardiff or Newport to Bristol or vice versa (and there are plenty of each though more of the former for socio-economic reasons) will find that it takes roughly 100% longer to do this by bus+train than driving. Thus turning a manageable commute into an intolerable one.
Even if you're fortunate enough to live and work within walking distance of rail stations at both ends with a direct train linking them it is hard to take. We recently had a colleague quit a job he was otherwise happy with after 4-5 years of commuting from Cardiff to Bristol under these conditions purely because he couldn't stand the GWR experience on the Cardiff<->Temple Meads route any longer. This was somebody who had previously commuted into London from Southend on C2C for years and so must have been pretty hardy. Unreliability, journeys constantly elongated by unpunctuality and overcrowding seemed to be the things that eventually tipped him over the edge.
Until there are expresses that do Cardiff<->Temple Meads in ~35 minutes 4 times an hour reliably, and intensive metro train/tram/whatever services in Cardiff/Newport/Bristol it is never going to be an competitive option. Sometime never, then...