I've found running crosses over hugely to cycling as a typical AGer (not elite/pro). Particularly for aerobic endurance - the leg endurance and cardio endurance you gain in running directly transfer over for aerobic (lower) level efforts on the bike that may have you going long.
The x-over decreases the stronger the cyclist you get, particularly the stronger you are a cyclist relative to your running as your legs get more specificity.
The x-over from cycling to running is a lot less, since the pounding on the legs in running will dramatically limit you even if you have a great cycling engine.
If I had limited time and could do predominantly run OR bike, it would be run hands down for triathlon racing.
I'll also note that being as good a triathlete as you can does NOT mean training S-B-R to be the best you can be in each sport - it really is S+B+R on race day, all in one and a good training program will reflect that. In particularly, expending a ton of effort to push to your near-limits in one particular sport will usually end up causing you to sacrifice too much in another one on race day in a triathlon to make it worth it. In triathlon, even a 90%/10% run:bike training ratio will dramatically outperform a 100/0% run:bike training ratio, and a 60/40 will crush both of those for most distances.
For the OP though: if your main "A" goal is to ride the fastest weekend event you can ride, pure cycling (no running) will outperform sacrificing some cycle time in lieu of running. (Running will not outperform cycling for training for a pure cycling event.) But if you are still interested in maintaining your running ability for a future tri,a smattering of running will minimally affect your cycling and still hold up a lot of run ability (wayyy more than zero running).
The x-over decreases the stronger the cyclist you get, particularly the stronger you are a cyclist relative to your running as your legs get more specificity.
The x-over from cycling to running is a lot less, since the pounding on the legs in running will dramatically limit you even if you have a great cycling engine.
If I had limited time and could do predominantly run OR bike, it would be run hands down for triathlon racing.
I'll also note that being as good a triathlete as you can does NOT mean training S-B-R to be the best you can be in each sport - it really is S+B+R on race day, all in one and a good training program will reflect that. In particularly, expending a ton of effort to push to your near-limits in one particular sport will usually end up causing you to sacrifice too much in another one on race day in a triathlon to make it worth it. In triathlon, even a 90%/10% run:bike training ratio will dramatically outperform a 100/0% run:bike training ratio, and a 60/40 will crush both of those for most distances.
For the OP though: if your main "A" goal is to ride the fastest weekend event you can ride, pure cycling (no running) will outperform sacrificing some cycle time in lieu of running. (Running will not outperform cycling for training for a pure cycling event.) But if you are still interested in maintaining your running ability for a future tri,a smattering of running will minimally affect your cycling and still hold up a lot of run ability (wayyy more than zero running).