When you say First abandoned various routes, most of them were contracted and won by TLC. The only routes TLC runs commercially in Bradford are the 653 (which First did abandon) and the couple of journeys a day on the 655.
I'm thinking about services like:
650 Bradford-Ilkley: A service that has never been replicated, and although there is plenty of capacity on the Northern half hourly trains this was a very useful service for when trains couldn't operate or were not timetabled, as well as obviously serving the sections of route where the stations are some distance away. So when trains don't run, travelling say from where I am in Baildon to Ilkley means either a direct service to Otley (653), then change onto a 62/X52/X84, or travel to Guiseley (737) change for Otley (33/33A) then as above.
652/3 Bradford-Otley/Harrogate: As it stands TLC did eventually pick up the slack, eventually offering an hourly Mon-Sat daytime service. But for quite some time they only offered a couple of journeys a day, and this service has been a mixture of direct from Bradford, only starting at Shipley and travelling via Baildon & Esholt. And now my wife just this morning informs me that TLC have posted notice that it will be withdrawn from July (I only hope Transdev are eyeing up the slack).
655/755 Bradford-Guiseley-Headingley-Leeds: Whilst not a particularly useful end to end service, from memory this still attracted decent loadings for intermediate journeys as these each ran hourly. They have never been replicated in any way.
656/7/8/9 Bradford-Baildon-Lucy Hall: Although TLC have taken on these routes, they run only every hour now leaving a large part of Baildon with very little capacity. The 626 Bradford-Baildon run by First does still operate every 20 minutes, but in reality serves on the main part of the village (technically a town now) and the west side as it weaves it's laborious route towards Shipley.
So quite a large part of the area (with a population of around 18K and growing) will from July see only an hourly bus service (the 737 Bradford-LBA usually single deck) operating anywhere near them, or half hourly services from Northern between Bradford and Ilkley. Compare this to just over a decade ago and there were at least 4-5 services per hour, several of which were operated by double deckers meaning for much of BD17 capacity has been severely reduced. This has translated into some shocking traffic problems which get worse every year, and of course impact on the remaining services.