How does run fitness translate to bike fitness

If you're in shape to BQ and running 50mpw, ramping up the bike will be a literal cakewalk. You will find aerobic cardio rides of 3 hrs almost no problem whatsoever from day one, and you can spend your time/energy on the bike building speed or even more endurance from there. 

I think it's a good thing you've built the run endurance and injury resistance - as said above, biking tends to come much faster, largely because the lack of pounding that requires well conditioned ligaments and tendons that takes months to develop if not years if you're new to it. 

But yes, for Vineman, definitely aim to increase bike fitness AND bike more conservatively this year, regardless of temp. And I feel your pain - I'm typically a top 5% run finisher in the amateur standings even in big tris like Vineman (overall, not AG), but despite me putting up my best bike training to date last year, I also melted down in the heat at Vineman, pretty spectacularly, actually.

But that meltdown wasn't all just race day misexecution - I intentionally shifted some  training from volume my run (my strongest) to the bike, thinking I could give up 10% on the run and get that 10% on the bike (with more time). What ended up happening is that I gained exactly what I thought I'd gain on the bike, but lost over double the expected amount on the run. That def won't happen again!

You have good answers here, but to add to it my personal experience is run fitness doesn't translate to bike fitness.  However I do seem to retain some run fitness from cycling.

IMHO, its not the fitness that is the issue, it's the muscles/body taking the usual time to re-adapt to the bike.  I've done 2 run focused programs for a HM where I dropped the bike.  I always found it a lot easier to get back on the bike and "get back up to speed" after a run cycle then from taking time off and doing nothing. Perhaps take a look at a bike focused program for the 1st half of your tri-training when you start it, then you can adapt to a more balance routine on the 2nd half.

Now you've done it.

I paced the bike last year right on plan, including backing off by a bit for the hotter day, so feel I executed that part well.  During the run I was right there on my first lap when the race leader, who was CRUSHING it, passed me on his last lap with about 5 miles to go.  He was hurting and stopped to put his hands on his knees and catch his breath, so I passed him.  He soon passed me again, but slowly and got to the turnaround ahead of me.  I saw his face as he ran by me in the other direction and he was digging deep just to hold on.  I caught up with him a couple of miles later as he was getting into the back of a car after pulling himself from the race.  That reinforced the need to slow down, hydrate and make good use of the ice at the aid stations.  I may have gone a little too far in these areas, but seeing him pretty much limp in the back of that car made an impression on me.

So, unfortunately I'm not hearing a resounding "Run fitness will translate into bike fitness".  I've got some decisions to make as my run training for the next 6 weeks up to the 50-miler  is pretty intense (maxing at 73 mpw) and I'm not sure how much bike I can put in that regime.  I did hop on and do a moderate 10 miles last Sunday and could really feel it in the Monday run.  The good news is that the moderate effort on the bike was still at IM distance speed, the looming question is, how long will that be sustainable as I lengthen the rides.  But it did sure feel good to get back on the bike.