It is not possible for the bus services between Aberystwyth and Aberaeron (the 40 and X50 services, at the time of writing) to connect with the trains at Aberystwyth. At least, not if you want to a regular interval timetable that is useful to other potential passengers.
Trains normally arrive in Aberystwyth at 20 minutes past the odd hours and depart 10 minutes later. If we assume that Aberystwyth station has a waiting room (it doesn’t, not yet anyway) then 15-20 minutes seems to be a reasonable time to allow for connections. If we use 15 minutes, the bus would need to arrive at quarter past (xx:15) and depart at xx:35. For 20-minute connections, the bus would arrive at xx:10 and depart at xx:40. With an every-half-hour service between Aberaeron and Aberystwyth, this means departures from Aberystwyth would be xx:05 and xx:35 or xx:10 and xx:40. The latter is actually the case at present.
The problem is that these times are not great for passengers wanting the X50 service (the one which departs at xx:10). Most university lectures finish on the hour, and getting down the hill to the station in 10 minutes is a tall order. It can be done, but you have to be fit and hope your lecture does not over-run. If the rail connecting buses were at xx:35, the result would be an even more useless timing of xx:05 for the other service. I imagine, many workers in the town also finish on the hour.
There’s another problem, too. Even supposing you don’t care about the university, the 40 route (to Carmarthen) takes 2hrs 15mins. Out and back would therefore take the bus 4hrs 30mins, so if you want to run an hourly service with five buses you only have half an hour to play with between trips. Arriving at Aberystwyth at xx:10 and departing at xx:40 would use all of that half hour, meaning the bus would have no waiting time at the Carmarthen end. This wouldn’t be good for delay recovery on the buses.
And retiming the trains probably isn’t possible, as they run through to Birmingham and have to slot in on the busy line between Wolverhampton and Birmingham. Plus, there’s little reason other than bus connection to want to retime the trains at Aberystwyth.