How do I best increase my average bike speed?

For now, I would just focus on spending as much time in the saddle as possible.  The more miles you put in, the stronger your legs will get and the faster you'll go. 

As you start to ride more and more, mix it up a bit with hills and flats.  Do rides where you ride steady and others where you do some shorter faster efforts.  As long as you stay consistent you'll get steadily faster.

Can't be said too much: ride more.

An exercise bike/spinner/time on the trainer can all be useful and are certainly worthwhile for increasing your overall fitness, but to get faster on the bike you have to get out on the road and put in the miles.

This may be a misquote, but when a reporter asked Eddy Merckx how he became a good cyclist he said;

'Ride lots'.

As others have said, it is not magic, ride as much as you can. Ride some easy, ride some hard, ride some hills and some long rides. Whatever you feel like that day, just ride. You don't need a structured training program at his point, just time in the saddle. When you have a 1000mi base, check back and let us know what your average speed is... then go ride some more. Good luck!

Ride a LOT...

I will add a couple other suggestions...  I found that after I rode a lot more and developed that good base, that adding some weight lifting, some MTN biking (which is also part of 'lots'), took some spin classes (more of the 'lots').  Those things also helped bring my leg strength up to par with my heart and lung strength = more speed for me...

I thought of a couple other options...

Lose weight - that will shirt the power to weight ratio in your favor...

Add a motor to the bike...

Ride lots is good.  I will add:

- ride hills, ride flats, ride everywhere
- Do high cadence work, do low cadence work
- Ride in the saddle, ride out of the saddle
- Work on technique
- Do some tempo work, some hard intervals; change things up

And of course, Ride Lots.

good plan.  Worked for me

I'll tell you what greatly helped me.  XC mountain biking. 

since the terrain isn't usually flat, or if it is you tend to have switchbacks, hills, turns its not a steady ride.  in the off season i do mtb.  after my next triathlon i will be doing some more mtb. 

its fun to switch it up a bit too.  road cycling is fun but mountain biking is much much more entertaining.

I think this is the best answer so far.  I'm not sure that ride lots is the sole answer.  Not that it is a lot by BT standards but last year I logged 1500 miles on my bike and my avg. speed barely changed through the season.  While I plan on logging lots more miles I think changing it up and adding variety will help. 

I'll also say this, you are not too slow for a group ride.  Find a ride with a no drop group and do your best to keep up with a few riders who are a bit faster than you.

This worked for me as well.

I biked over 3.5k miles last year and really didn't seem much increase in speed.  I recently mixed things up with MTN biking, spin class, in and out of the saddle work, etc.  A lot of things to keep it interesting.  Took some notes on Jorge increase power thread...

After a couple of years with little gain (but GREAT base), I quickly made a jump in speed the last few months.

that was me also.  this is florida so the trails are limited but there is a park with 14 miles of trails and i used to go in off-season.  it seems much shorter but the entire park takes about 3 hrs to ride due to the difficulty of the terrain.

ride at least 4x/week.

mixing up the workouts as others have indicated.

make sure you do 1 recovery ride per week, nice easy pace.  one tempo ride, some intervals, some hill repeats....keep mixing it up.

keep things interesting.  you ride 4x per week, even just 1-1.5 hours per ride, your speed will increase very quickly.

Also, some advice that helped me, was not to even look at speed.  Ride based on your RPE or HR....I was so concerned about MPH when I first started, every ride was too hard an effort.....