Hardest thing will be finding taps that match your basin taps. Unless you're not overly fussy. If you are might be a good time to update the taps for both the bath and basin as it makes a big different to the overall look.
Cost to change all won't be much more than changing just the bath.
Judging by the tap design they've not been fitted recently so guessing you won't have isolation valves. Might be worth asking the plumber / handyman to fit these too at the same time, will make it easier in the future.
As for price, depends on your area and whether you get an actual plumber or just a handyman type person. Its not a big job so you might struggle getting someone to bother coming out!