Main thing is you have gone out and done it, the speed increase will come naturally, not just with the new bike, and you will go further, faster and for longer before taking a break without you even realising it.
When I first started in August I did a 4 mile route with 2 breaks, went up to 9 mile route of Richmond Park with 2 breaks, then rode to Richmond Park and back on a 17.9 mile route with 2 breaks. Jumped to a 35 mile route with 1 break and finally did a 55 miler with 2 breaks. My speed has pretty much settled on 13.7 mph but having maintained that over longer distances it has been satisfying enough.
1 thing I have learnt, compare to your own results, not to any speed demons on Strava etc. It can be disheartening to see yourself in the bottom 35% of segments etc, so I tend to just ignore all that and concentrate on how I did this time to last time, and appreciate the natural progression of improvement.
Most of all enjoy it, one of the wonders I have found with bikes is seeing areas in a new way, and visiting places I would never have normally driven through in my car. Beats the gym in every way imo!