No way Bledsoe makes the HOF. He'll have a few things working against him:
1) Tom Brady came right after him and outperformed him in just about every way possible. Not saying that it's fair for that to enter the equation, but it will.
2) His greatest claim to the HOF is the volume stats that he put up. Unfortunately, the generation of QBs that came after him--Brady, Manning, Brees, Rodgers, etc.--are rewriting the record books in those same categories. Manning, Brady and Brees have already passed him on the career passing yards list, and Eli, Big Ben, Rivers, Romo, Schaub, Rodgers, Cutler, Stafford, and Matt Ryan all have a shot at it. I'd guess that at least 3 or 4 of that group will, maybe as many as 6 or 7. 17th on the all-time passing yards list looks a lot less impressive than 7th.
3. He wasn't a terribly efficient QB. His sack percentage was way too high (from 1998 onward, he never did better than 7%). His 3.1% INT% is right up there with the Eli Mannings and Brett Favres of the world. His completion percentage was downright pedestrian. His TD/INT ratio wasn't that good. etc. etc.
4. He never won a Super Bowl
5. He retired too young
So no, I'd say that he won't make it. In an alternate universe, maybe he could have stuck around, won a SB or two at the end of his career on the back of a superior running game, and ridden that into the HOF like Elway did, but that's not how it worked out for him.