Getting faster on the bike for someone very slow

There are several bike workouts to increase speed.  Look up some of them and try to incorporate them into your workout.  The easiest way to increase your speed is to increase your mileage.  With having a higher mileage base your speed will pick up.  Also bike more often.

Slicks are the biggest improvement you can make.  Next up is to strip everything that is not necessary to the race off of the bike for the race.  Is the course hilly or flat?  When flat or descending, tuck down to the bar as much as you can.  It's a huge difference between sitting bolt upright and laying down on the bars when descending, it's free, learn to do it.

That's about all you can do in 3 weeks.  It's not enough time to improve your fitness much, but the other thing is time in the saddle.  Put more miles in the saddle, and those miles should be spent working.  Climbs are your friend.  About twice a week, you should be riding with a specific goal in mind.  These are your quality workouts.  Either working on endurance, strength or speed.  The other rides are recovery and you can take it easy on. 

But 3 weeks may not be enough time to get acclimated to someone else's bike.  For a shorter race, not a big deal, you can probably get away with it.  But for a longer race I'd rather see some more time in whatever other bike you would ride.

The commuter slicks will make a huge difference.  If you go that route just make sure you get a few good rides on them to not only get used to them but also to wear off the waxy stuff that comes on new tires.

http://www.performancebike.com/shop/profile.cfm?SKU=15304&subcategory_ID=5430

I assume you've looked at the engine for efficiency as well?  For example, do you know what cadence you ride?  Strange as it seems, riding at 90rpms  makes it easier to ride faster than riding at 60 rpms - but I've seen many slower cyclists riding those slower cadences.

Seems you're in great cardio shape, and you can't change strength or those variables in 3 weeks, but cadence is one thing you can work on.

P.S.  I have the same problem, but for swimming!!  Plenty of aerobic conditioning, plenty of muscle strenght - I'm just slow!  So I'm trying to figure out what I'm doing wrong in form or efficiency there.

That was my first thought as well.  I did my first year of triathlons on a mountain bike with knobby tires.  I wasn't fast, but I was as fast as I could be.  Before the race, I got a cheap Cateye bike computer that gave me my speed and cadence info, and worked on keeping my RPMs in the ~90 range.  I think my avg race speed was around 13.5 mph.  I wonder how much faster I would have been with slicks? 

Great price!

I was at my local bike shop when someone called with the same situation. The bike shop owner told her he was so confident it would make a big difference as to improving her pace that he would take them back and refund her money if they didn't work. He quoted her they would cost about $50.  

Thank you for mentioning that!  I'm glad I have the patience to read through these and wait to respond.

And the bike to borrow would be a road bike, not another mountain bike.  Just saying.

Those curly bars on road bikes aren't just for good looks!  They give plenty of positions to move your hands around.  For mountain bikes, you have less options.  The pain will lessen as you get more time on the bike and your body adapts.