Similar to the rock guitarist, the chances are that the guitarist has started out either with a guitar package from a shop (including a guitar, amp, strap, lead, plectrum and tuner) or has been given a second-hand guitar. Blues guitarists seem to have a way of ending up with used guitars - I think that's just the way of the world.
I've included some easy links for purchasing from Amazon.com and Amazon.co.uk at the bottom of the page. Don't want to read the rest, then go straight to the gifts in the US or the gifts in the UK.
Here's what you can get either guitarist:
A set of picks - buy a variety of picks. By the way, pick and plectrum are the same thing. Beginner guitarists and even intermediates are still finding their way around the different picks. Get a few thicknesses of each of the following: Dunlop Tortex, Dunlop Jazz II, Dunlop Jazz III. Maybe even get a copper pick. Don't bother with some famous brand on the pick, they're usually just regular picks with an image on so they can charge more.
Strap locks - if their guitar is worth less than $400/£200, then plastic locks (e.g. by Dunlop) are good enough. If it's worth more, then get some Schaller metal locks instead.Slide - every blues player needs a slide. They may not use it all the time, but they will use it now and again. Some even use one every song. They should at least have a glass slide and a metal slide.
New Strings - They should be changing them on a regular basis. Play safe and buy what they use or take a chance or get them some great strings and see how they react after stringing up. Since this is for a blues guitar, the strings tend to be a bit thicker than the out-and-out speed merchants. As for gauge, go for 10s to be safe. Better still try the gauge 10 light tops, heavy bottoms. Rotosound do some nice sets with this mix.Strap - Again, another personal preference. I like Leather or Leatherette with a padded strap for the shoulder and front of the guitar then tapering down to a thinner end for the back. I just go for plain black, but what's the guitarist interested in? Look around and you can find almost any design for a strap (skulls, football, alcohol brands, motorcycles, bandnames, roses, paisley and so on). Avoid elastic or stretchy straps unless you know they like them - it's a lot harder to play guitar when it's bouncing on a bungee rope.
Cable or Lead - Buy a decent lead. You don't need to spend lots. Avoid the cheap coiled leads. Not all coiled leads are rubbish, but we can discount the majority. We're aiming for repairability, so get a lead with a non-moulded plugs. Something like a 15-20ft length will let the guitarist move around. I've had my last guitar lead for over 15 years and only retired it last year.Part of an in-depth series looking at gift and present ideas for guitarists.