Can You Put Mending and Infinity on a Bow in Bedrock? No

Why not

Mending and Infinity can each go on a bow, just not together. Here is what a bow can take instead: Curse of Vanishing, Power, Flame, Punch, Unbreaking, Infinity, Mending.

What that means in practice

This is one of the best-known conflicts in the game. Infinity names Mending as incompatible, so the two can never share a bow. The choice comes down to what you run out of first: arrows or durability.

Which one to pick

You can't have both on one bow. Pick Mending if you have arrows to spare, Infinity if you don't.

Early game. Infinity. The enchanting table can offer it, arrows are scarce, and you have no XP farm to feed Mending yet.
Skeleton or mob farm. Mending. Kills drop arrows and experience, so the bow repairs itself while you collect ammo.
Long exploring trips. Infinity is simpler. You only carry one arrow, which frees inventory space for loot.

The Mending vs Infinity comparison goes through every situation, with the numbers for both.

Why the game says no

Both enchantments can go on a bow on their own. Each one lists the other as incompatible, though, and that is enough to block the pair. So the anvil skips the second one and never puts both on the item. Also, the enchanting table never offers both in one roll.

Bedrock keeps these rules in its own built-in lists. The full list of clashes is on the incompatible enchantments page.

The max build with each

With Mending, a max bow has Power V, Flame, Punch II, Unbreaking III and Mending. In the cheapest order it costs 26 levels over 5 anvil steps, and no step goes above 9. Open it in the calculator.

With Infinity, a max bow has Power V, Flame, Punch II, Unbreaking III and Infinity. In the cheapest order it costs 29 levels over 5 anvil steps, and no step goes above 10. Open it in the calculator.

The best bow enchantments page explains every book, and the bow enchant order shows each anvil step.

Where Mending and Infinity go

Mending goes on helmet, chestplate, leggings, boots, elytra, sword, axe, spear, mace, trident, bow, crossbow, pickaxe, shovel, hoe, fishing rod, shears, brush, flint and steel, shield, carrot on a stick and warped fungus on a stick. The enchanting table never offers it, so every one of them needs a book. Related questions: Mending on elytra, Mending on shield, Mending on trident, Mending on spear, Mending on mace, Mending on crossbow, Mending on fishing rod, Mending on shears, Mending on pickaxe, Mending on helmet, Mending on flint and steel, Mending on brush.
Infinity goes on bow. The enchanting table can offer it there directly. Related questions: Infinity on crossbow.

Commands and creative mode

The /enchant command refuses the second enchantment, because the pair is incompatible. Bedrock's /give can't add enchantments either, so there is no command shortcut. The command generator writes the right syntax for your edition.

Java and Bedrock

As far as the item list goes, the answer is also the same in Java and Bedrock. The anvil differs, though: Bedrock only charges for the levels a book adds. This page follows Bedrock 26.60.

About Mending

Mending repairs an item with experience orbs. When you pick up experience while holding or wearing a Mending item, the XP goes into repairing it first, at 2 durability per XP point.

Mending has a max level of I. If you need a book, you can get it from librarian villagers, trial chamber vaults and enchanted loot from fishing and chests. Before you buy, read everything about Mending, including what each level does.

About Infinity

Infinity lets you shoot forever with a single normal arrow in your inventory. Special arrows are still used up.

Infinity has a max level of I. If you need a book, you can get it from the enchanting table, librarian villagers and enchanted loot from fishing and chests. Before you buy, read everything about Infinity, including what each level does.

What else a bow can take

Besides Mending and Infinity, a bow can take Power, Flame, Punch and Unbreaking. Then the best bow enchantments page ranks them and gives the max build.

Related questions: Mending on bow, Fire Aspect on bow.

Questions

Can you put Mending and Infinity on a bow?

No. You can't put Mending and Infinity on a bow together. They are incompatible in Bedrock 26.60, so a bow can only have one of them.

Which is better on a bow, Mending or Infinity?

Mending if you have an arrow supply, because the bow then lasts forever. Infinity if you don't, because you never run out of normal arrows.

Can a crossbow have Mending instead?

Yes. Crossbows can't take Infinity, so Mending fits a crossbow with no trade-off.