Having owned both a LH 405 and 410 (as well as RHD 405, 405DH, 409 & 411), I can say Bristols are very hard to buy and very hard to sell. If a buyer has their heart set on a particular car in a particular condition, it can take years for it to pop up. Indeed often these are called "widow's cars" because they only come up for sale after the funeral.
However, if you are trying to sell a Bristol, it also can take years. I realise this is not answering your question the way you hoped, but that's the reality of the market. It's too small. The cars are too rare. The profile is too low. It consists of bottom feeders (start at $1 on eBay with no reserve), enthusiasts (who unfortunately are greying, but already are members of these forums and/or the club) and eccentric rich guys who appreciate something no one else knows about. Pick your market and structure your marketing and your expectations accordingly.
Regarding LHD, at one point, while living in the USA I could have bought a LHD 401, 402, 403, 404, 406, 407, 408 and 409, to add to the LHD 405 and 410 I already owned, practically cornering the LHD market, but except for the 402 and 404, they were all cheap (nothing over $10,000). But at the time I was moving to New Zealand, thus was in slim-down mode.
I amassed a collection by accident, meaning when I came across Bristols not in the Club Register, I would let Bob Charleton know, and eventually he appointed me a registrar for North America. I routinely would ask owners for details on their cars, including what they paid, or if it was for sale, what they were asking.
An owner of a $35,000 car would say "if I can get $7,000 for it, it's gone" because after advertising they got no buyers and the car would have been sitting in the garage gathering dust because their lifestyle changed. So I would write a cheque for $7K, enjoy it for a few years while leaving a trolling line in the water, eventually attracting an enthusiast prepared to pay $35,000 - indeed thrilled to because it was just what they were looking for, and it was the only one available anywhere in the world. This is how I justified to my wife that my car collection was not an addiction, since it never took money out of the family budget, but paid for a few nice holidays overseas. When Bristol Cars finally closed, meaning parts were now an orphan market, I sold my last Bristol, a RHD 411 for $32,500 and replaced it with an aluminium-bodied X350 Jaguar that cost me $5,000 and rides like a dream.
The point?
The Bristol market is too small to have any reliable valuations. It truly is a market made by two people wanting the same car, or one bitten by the bug and no other equivalents are on offer anywhere.
LHD opens up Europe and North America which means a statistical population over 1 billion, but the awareness of Bristol as a car is miniscule. Ebay will expose the car to many viewers, but the premium auction houses get a higher concentration of high bidders... provided you have two rich guys lusting after it.
SLJ Hackett serves the "in-the-know" market, pricing vehicles so they stay in business. If you are in a hurry, consign it with them. Except that as a LHD vehicle you probably would be better sending it to one of those California classic car dealers that advertises in things like the Robb Report, Jetset Magazine or JustLuxe. I've not been following the US market, so I don't know the who's who in the US bling business selling classic cars at inflated prices.
If you prefer trolling (the fishing analogy not the internet one), look at the auction sales and add 20% after assessing your car's condition - then prepare to wait for years, unless you get lucky. If you troll the USA, add an additional 20% for LHD but include free shipping (RO/RO) in the price. Your likely buyer will be in New York or California. Then decide how low you will go, and wait until you hook the buyer and reel him in.
Best of luck and keep us posted when it sells.