It's a little bit wider than you found:
So, you will have one feat from level 1, one from level 3, and one from level 6 for three in total.
All Bloodline Feats from Dragon Compendium & Dragon Magic have the wording:
Prerequisite: Ability to cast arcane spells without preparation.
On a technicality, Beguiler qualifies, so they can take it, if the GM allows, as they are non-prepared arcane spellcasters. Your level 1 feat is taken.
Next comes the 3rd level class feature:
Advanced Learning (Ex): At 3rd level, you can add a new spell to your list, representing the result of personal study and experimentation. The spell must be a sorcerer/wizard spell of the enchantment or illusion school and of a level no higher than that of the highest-level spell you already know. Once a new spell is selected, it is forever added to your spell list and can be cast just like any other spell on your list.
At earliest at 4th level you are allowed to have 4 Ranks of Knowledge (Religion) as that is not a class skill, so at level 6, you may take Arcane Disciple from Complete Divine, p.79, to gain a whole slew of domain spells.
Prerequisites: Knowledge (religion) 4 ranks, Spellcraft
4 ranks, able to cast arcane spells, alignment matches your
deity’s alignment.
Benefit: Add the chosen domain’s spells to your class list
of arcane spells. If you have arcane spellcasting ability from
more than one class, you must pick which arcane spellcasting ability this feat applies to.
At this point, your level 3 feat is still free. So you have two options:
- in theory, Extra Spell, Complete Arcane, p. 79. That's the boring option adding one spell to your spells known, but you should in theory take it from your spell list, and you know your whole spell list already - so you might need to negotiate with the DM to add a spell there. Since your 6th level feat will be Arcane Discipline, and your 1st level one is a Dragon Bloodline feat, you can only take this once at best anyway.
- Mother Cyst, Libris Mortis: The Book of the Dead, p. 28. This is the more exciting option and grants not one but over time 4 spells. You need to raise your Knowledge Religion to 4 anyway for Arcane Discipline, so the 2 ranks prerequisite is "free". You gain the following spells in the end: 1st—necrotic awareness; 2nd—necrotic cyst, necrotic scrying; 3rd—necrotic bloat.
However, there are also items and pacts to populate your spell list a tiny bit more:
- Knowstones, Dragon Magazine 333, p. 93, add their inscribed spell to your spells known.
- Runestaffs, Magic Item Compendium, p. 223. They contain specific spells and allow you to cast them using your own spell slots.
- A Dragonpact under the Rules from Dragon Magic, p. 87, grants a couple of Spelllike Abilities from outside of the spell list at the cost of a spell slot.