I'm playing the Psilons and I'm at war with the Silicoids.
I have superior techonlogy and easily wipe out their ships, but against their planets with 10 or so bases I hardly make a dent.
I designed a small bomber for the express purpose of destroying the ground bases: Computer 0, Shield Class 1, ECM 0, Zortium I armour, Fusion Engine, Class IV Manover, Inertial Stabilizer, and 1 Fusion Bomb.
Stats: Shield 1, Beam Defense 8, Missile Defense 8, Speed 4, Attack 0
The plan was to have very mobile ships armed with bombs destroying the bases, but 50 of them only do like 1-5 damage, hardly making a dent. One mistake may have been to have no Computer, and thus an Attack value of 0, but for some reason I though it didn't apply to bombs.
The Silicoids also have the Class X Planetary Shield tech. The missile bases have 75 hit points and a Shield of 15.

So, any good tactics to use against those bases?
Should I just concentrate on destroying the ships instead, then retreat and send in the ground troops? The bases seem to ignore transports.

You'll want something better than a fusion bomb. Do you have any high-powered missiles, or is there a better bomb tech in your weapon tree?

I'm researching Anti-Matter torpedoes.
In the meantime the best tactic seems to be to send in a huge battleship on hit and run missions to reduce the number of missile bases.

Huge battleship with 11 Anti-Matter Torpedoes, Anti-Missiles device, and Auto-Repair cracked the nut. :-)

Spies, though you don't know when they're going to make their strike, or at what planet.

Spies are too random. I prefer using them to steal tech. That was one of my favourite tactics in Civilization too.
So far the best tactic seems to be to build a huge ship, load it up with whatever anti-missiles and repair devices you have, and then spend the rest on the most damaging missiles and/or bombs, and christen the ship SS Nutcracker.

Yeah, spies only work okay for that when you're at the point that you can pick and choose which planets to invade - and have a bunch of active spies. But it's an option.

Do lasers which halve the target's shields also work this way against missile bases?

I found mass drivers are quite effective, just conquered a race using 100-200 ships with mass drivers only (they destroy 1 base every 1/2 shots). Basically I have no weapons, only mass drivers.

I don't know really how battle works, but I think the way shields mitigate damage, is less effective against mass drivers.

seems to be like

if 100 weapons do 1-5 damage and enemy have damage mitigation of 4 the average number of damage is just 20.
Mass drivers do nominally maybe only 50 damages but those damages are done only once so 46 damages in total,

on paper 100 weapons are 100-500 damages => effectively 20

on paper mass driver 50 damage => effectively 46

(I don't know if that is really true, or if work really like that.. I just tried mass drivers and they worked well, that's all XD)