I'd suggest interval training but perhaps not at this stage. Instead I'll offer "fartleks"...these are similar to intervals without the rigid structure of intervals...used generally by runners but easily used by all sorts of activities.

Basically the principle is unstructured intervals. Use a known and often ridden loop, out and back, etc. ride of an hour to an hour and a half. Start with the usual warm up...I usually use 10 minutes of easy pedaling then 5 minutes at a higher level to start a "sweat". After that I will use 15 to 30 second "attacks" with full recovery between. I will go from a hay bale, telly pole, etc. anything...the spirit is unstructured intense, but not heart stopping, periods of activity with full recovery between. On an hour ride I use the middle 30 minutes for the fartleks followed by 15 minute cool down ride home. I would do this once a week.

This is not for race training by any stretch unless it is to get over staleness, over training, etc. This is more in line with beginning to increase overall speed.
Do this once a week and use a simple notebook to chart progress...more like...after two weeks do the "attacks" feel any easier?...do you recover faster between?...has your "attack" speed increased?...etc.

It may take 4 to 6 weeks to see an appreciable increase in overall speed.

Keep us posted if you try these and how they work out for you.