That is a great experience & travel report.
Happy travels.

Cost will be less than India.
ATM's - There is an ATM at Zia Airport, just after the passport counters on the facing wall alongside the money changers. We had no problem finding ATM’s during our trip (not one on St Martin’s) and found the Dutch Bangla Bank ATM’s the most reliable. We took an emergency reserve of US$ cash but didn’t need to use it.
Taxi from airport - Due to a lengthy flight delay we arrived into Dhaka late evening so decided to throw ourselves at the mercy of the pre-paid taxi counter. Actually it was fine, the guys were good fun and we thought it was worth the extra Taka for the convenience. The counter is as you exit the airport to the left, they will complete a form for you with details of your destination and number of bags, then you pay them a 50T booking fee with the 500T (that was the rate to the Ramna) paid to the taxi driver at your destination. Yes for sure it will be cheaper if you exit the airport and pick up a cab outside but for the difference in price sometimes it is worth paying a little more for the comfort and convenience on arrival.

A pleasure to assist - hope you have a great time there - photographically, it's got so much on offer - take a good camera; a good lens and lots of memory cards.
Cheers
Zoltan

Bangladesh is more easier for a solo female travelers then India though as a white or western women except more attention from man as its part of the subcontinental culture.
Use common sense,stay alert and follow the proper precautions when talking to stranger (and there will be many who might try to be friendly) its advisable to keep it short and not reveal much about your plans or business (some would want to spend more time with you or show you around...they might just be polite...but avoid it.
You will be stared at anyways and Shalwar Kameez isn't guaranteed to prevent things but it helps.
Subcontinental man don't think that white re sluts,they do think they re easy with sexual relationship and hence will try their luck so try not to be over friendly.
And also do not except any help,drinks or DINNER from stranger particularly in the streets and don't leave your drink unattended and if some one feels avoid him.

Hello there Nat,
To respond to your queries:
What are costs like compared to India?
Cheaper than India when it comes to most things; accommodation,food,shopping...however, alcohol isn't that widely available and are pricey in the big hotels. Being a foreigner, you will have the advantage of purchasing them cheaply from bonded warehouses.
Can I use an ATM at Dhaka international airport?
Depending on the bank, but seldom there have been any problems with travellers...regardless of the type of card they had.
What currency is best to take - USD? Seems like TCs are a waste of time??
USD still dominates, and USD TCs are a safer bet, in case you lose them.
Arriving at 16.30, what are my options to get into Dhaka? Are there prebooked taxis?
Plenty of options, taxis being one of them.
Where would you recommend staying in Dhaka itself? As I am on a 2 week holiday I am no longer on my 2 dollar a day budget (!) but at the same time want somewhere good value and safe.
Any hotel/guesthouses in the Gulshan,Baridhara,Banani and the adjacent areas should cater to you with extra comfort...which obviously will charge you extra as well.
Hope you have a nice stay there!