Saddlebag Laptop advice
I have carried a laptop on my commute bike for closing in on 15 years now. Mainly in panniers (saddle bags). For a little while in a courier bag when when I was young and dumb. For what it is worth (aka the dangers of anecdotal evidence) I didn't have any laptop failures directly related to a bike trip.  I even toured with a 17inch laptop across 800 km of mixed terrain (road and dirt) in Norway with out incident (riding to a workshop and conference).  That laptop is still going strong 5 years later.


Waterproof pannier.  Water is the enemy of most electronics. So is dust.  It pays to be able to keep things very well sealed.
Well padded case. I used to use a well padded sleeve to house the computer and moved to a pannier with a built in padding.
Strong mounting. Not all bags are created equal.  Get ones that have rigid re-inforced back plate and strong mounting system. You don't want the bag flopping around.  Cheap panniers can sometimes twist into the spokes which will likely result in damage to your laptop during the ensuing carnage.
Strong pannier rack.  As a corollary to (3) if you have a cheap flexible rack this could also cause problems, but I haven't personally had any problems across a variety of rack types. Some racks also support panniers against twisting better than other racks.
Back it up just in case...  This is really good advice regardless of transportation method.  I always keep at least two backups going, one in the office and one at home (offsite).  I once came into my office to observe my desk under water.  If I had left my laptop there I would have lost it and the backup sitting on the desk. 


Other Deep thoughts...

I have always wondered about the impact of vibration, but so far I haven't seen any clear indication (warning anecdotal evidence).   I had one hard drive die spontaneously while working on a report. Perhaps vibration shortened its life?  It it was also very hot that day and I was without air conditioning and I was running some simulations so the temperature could have fried it too.

I have also had a lust for well built laptops, which may have stood up better.  I am a hipster poser so you can guess which brand of computer I have continually purchased.