Is BULB offering a installation service of any smart thermostats, like most other energy companies are doing?
No, they are not.
Why is BULB is not offering or selling smart thermostats to their customers?
I suspect because they have a lot on their plate right now.
If we buy our own smart thermostat, is BULB offering to install the smart thermostats for their customers, as this is another way of saving energy.
They are not, no.
Smart thermostats being offered by energy companies is an interesting one.
Scottish Power offer the Climote sytem
(rebranded as the Scottish Power Connect) as a monthly cost for customers, and really this is another money grab.
They charge £180 or £304.56 over two years for a system which personally I'd say is not worth more than £100 for the hardware and maybe £40 for installation. After the two years, I believe you have to pay again
as the system is sold on a subscription model
Nobody offers things for free. Either the government gives them incentives to do something (money for the rollout or fines if they don't), or they charge an excess for the system to make more money themselves off customers.
Also remember that energy companies make money by selling you energy. If you stop using as much energy, they don't make as much money...
If you'd like a Nest thermostat (or similar), you're best off buying it yourself (they can be around £150 on sale) and then getting a local tradesman to fit it if you're not happy doing it yourself. You don't need to be an electrician to legally fit a thermostat like this.
I do however agree with @linesrg above. I have a Nest and although it's nice for the remote access, it's not going to save you any money over a traditional thermostat. Even if the auto-away features turn the heating off when you're not there, there's a lot of difference in cost to make up with savings on energy.