Now that the Advance Class Guide is out, the answer has changed (as @Lord_Gareth suggested it would in his January 2014 answer).
And now that the ACG errata is out, the answer has changed again. Changes incorporated below.
As of today, there are two published feats (three if you include Mythic) that expand the set of finesse weapons:
1. Dervish Dance
(which requires a 13 DEX, Weapon Finesse, 2 ranks in Dance, and proficiency in the scimitar) lets you count a scimitar as a finesse weapon (and add DEX instead of STR to damage)...as long as it's sized for you, used one-handed, and you aren't "carrying a weapon or shield in your off hand."
2. Slashing Grace
(which requires a 13 DEX, Weapon Finesse, and Weapon Focus) lets you use DEX (instead of STR) for damage with any one handed or light slashing weapon one has Weapon Focus in. As with Dervish Dance the weapon has to be sized for you. Additionally (since the errata)
You do not gain this benefit while fighting with two weapons or using flurry of blows, or any time another hand is otherwise occupied.
Note though that it doesn't allow one to use DEX to hit with a one-handed slashing weapon unless one has at least 1 level in swashbuckler. Swashbuckler's get the Swashbuckler's Finesse ability which says:
a swashbuckler gains the benefits of the Weapon Finesse feat with light or one-handed piercing melee weapons.
That combined with this text from Slashing Grace:
When wielding your chosen weapon one-handed, you can treat it as a one-handed piercing melee weapon for all feats and class abilities that require such a weapon
lets swashbucklers (but not others with Weapon Finesse) use DEX to hit with a longsword or similar weapon. (A fighter with Weapon Finesse and Slashing Grace gets DEX to hit with her rapier but still uses STR for damage. If she switches to a longsword she gets DEX to damage but is back to using STR to hit.)
Also note (as per the original question) that Slashing Grace makes a bastard sword a finesse weapon for swashbucklers...but only while wielded one-handed.
Bucklers and Swordsmaster's Flair are OK!
The following FAQ was asked about Slashing Grace but applies to Dervish Dance as well.
What exactly does it mean that “You do not gain this benefit while fighting with two weapons or using flurry of blows, or any time another hand is otherwise occupied?” Can I use a shield? What about a buckler? Can I use flurry of blows? Brawler’s flurry? Two-weapon fighting? Spell combat? Attack with natural weapons? What if I throw the weapon? What about swordmaster’s flair?
Slashing Grace does not allow most shields, but bucklers work because they don’t occupy the hand. Flurry of blows, brawler’s flurry, two-weapon fighting, and spell combat all don’t work with Slashing Grace. Attacking with natural weapons beyond the weapon you chose for Slashing Grace also does not work. Slashing Grace only works with melee attacks, not thrown attacks with a melee weapon. Swordmaster’s flair should have a sentence added to it that says “Carrying a swordmaster’s flair counts as having that hand free for the purpose of abilities that require a free hand, though you still can’t hold another object in that hand.”
Why No Love For Rapiers?
As an aside, Jason Bulmahn (Lead Designer) has said that DEX to damage was a late addition to Slashing Grace, and the design team didn't realize that it made a longsword significantly better for a swashbuckler than the more iconic rapier. To solve that, they've announced that the following feat will be released in the upcoming Pathfinder Player Companion: Advanced Class Guide Origins:
FENCING GRACE (COMBAT)
Your extreme style and fluid rapier forms allow you to use agility rather than brute force to fell your foes.
Prerequisites: Dex 13, Weapon Finesse, Weapon Focus (rapier).
Benefit: When wielding a rapier one-handed, you can add your Dexterity modifier instead of your Strength modifier to that weapon’s damage. The rapier must be one appropriate for your size.
In addition, if you have the panache class feature, you gain a +2 bonus to CMD against attempts to disarm you of your rapier while you have at least 1 panache point.
Mythic note: one more way to get DEX to Damage
While the core of this question is about adding to the set of finesse weapons, both Slashing Grace and Dervish Dance also add DEX to damage (arguably their bigger benefit). For completeness, I'll add one more DEX to damage option: Mythic Weapon Finesse.
If you happen to be playing with the optional Mythic rules, this is generally the best solution. The Mythic Weapon Finesse feat's only requirement is that you already have the general Weapon Finesse feat. It states,
When using Weapon Finesse, you may also use your Dexterity modifier instead of your Strength modifier on your damage rolls.
So (unlike the options above, you can use any shield, flurry of blows, all of your natural attacks, etc.). It even tacks on the further benefit that > If you carry a shield, its armor check penalty doesn't apply to either the attack rolls or the damage rolls.
Best Answer
Heroes of Battle is the place for the most updated siege rules, including a number of feats (Ballista Proficiency, Expert Siege Engineer, etc.). The relevant feats may be selected as fighter bonus feats, so that makes fighter a possibility here. Fighter is also good for getting crossbow feats—the rules do not specify that feats relating to crossbows apply to ballistae, despite being just an over-large crossbow, but if allowed, fighter is in a pretty good place to get them.
Dragon vol. 295 has a 3.0 prestige class, master siege engineer. As it predates Heroes of Battle, it doesn’t interact with those rules directly, and its abilities are most potent when dealing with multiple siege weapons used by multiple crews. Nonetheless, it does exist.
Back to Heroes of Battle, the legendary commander prestige class may be worth considering. It requires Leadership and expands on one’s ability to command troops. Leadership may even be appropriate for once since siege weapons require crews (ideally two for light ballistae, four for heavy ballistae, in addition to the crew leader).
Dragon vol. 310 provides a number variant fighters, including targeteer which gains proficiency in two ranged exotic weapons—Heroes of Battle does not define ballistas as exotic weapons, and Ballista Proficiency is distinct from Exotic Weapon Proficiency, but it’s a minor stretch to consider it. Alternatively, the commander variant in the same article may be more appropriate.
The commander and targeteer have different bonus feat lists from the base fighter, but it only covers core feats—it seems to me that non-core feats should be added to the list as appropriate, and these siege weaponry feats are appropriate for these variants. If the ruling is that they cannot be added, though, then of course you don’t want anything to touch that feat list, and base fighter is ideal.