Depth Strider and Frost Walker on Boots in Bedrock? No

Why not

Depth Strider and Frost Walker can each go on boots, just not together. Here is what boots can take instead: Curse of Binding, Curse of Vanishing, Frost Walker, Protection, Blast Protection, Fire Protection, Projectile Protection, Feather Falling, Soul Speed, Depth Strider, Thorns, Unbreaking, Mending.

What that means in practice

Both deal with water, so the game makes you choose. Depth Strider speeds you up in water, while Frost Walker keeps you on top of it. Both work with Protection, Feather Falling and Soul Speed on the same boots.

Which one to pick

Depth Strider for most players; Frost Walker for crossing water on foot.

Ocean monuments. Depth Strider III. You fight and mine underwater, where Frost Walker does nothing.
Crossing rivers and lakes. Frost Walker. You walk straight over the surface instead of swimming.
Building underwater. Depth Strider, together with Respiration and Aqua Affinity on the helmet.

The Depth Strider vs Frost Walker comparison goes through every situation, with the numbers for both.

Why the game says no

Both enchantments can go on boots 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 Depth Strider, max boots have Protection IV, Feather Falling IV, Soul Speed III, Depth Strider III, Thorns III, Unbreaking III and Mending. In the cheapest order it costs 66 levels over 7 anvil steps, and no step goes above 16. Open it in the calculator.

With Frost Walker, max boots have Frost Walker II, Protection IV, Feather Falling IV, Soul Speed III, Thorns III, Unbreaking III and Mending. In the cheapest order it costs 64 levels over 7 anvil steps, and no step goes above 16. Open it in the calculator.

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

Where Depth Strider and Frost Walker go

Depth Strider goes on boots. The enchanting table can offer it there directly.
Frost Walker goes on boots. The enchanting table never offers it, so it always comes from a book.

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 Depth Strider

Depth Strider makes you move faster in water. Each level removes a third of the water slowdown, so level III lets you walk underwater about as fast as on land.

Depth Strider has a max level of III. 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 Depth Strider, including what each level does.

About Frost Walker

Frost Walker turns water under your feet into frosted ice as you walk, so you can cross oceans on foot. It also makes you immune to damage from magma blocks and campfires.

Frost Walker has a max level of II. If you need a book, you can get it from librarian villagers and enchanted loot from fishing and chests. Before you buy, read everything about Frost Walker, including what each level does.

What else boots can take

Besides Depth Strider and Frost Walker, boots can take Protection, Blast Protection, Fire Protection, Projectile Protection, Feather Falling, Soul Speed, Thorns, Unbreaking and Mending. Then the best boots enchantments page ranks them and gives the max build.

Questions

Can you put Depth Strider and Frost Walker on boots?

No. You can't put Depth Strider and Frost Walker on boots together. They are incompatible in Bedrock 26.60, so boots can only have one of them.

Can boots have Frost Walker and Feather Falling?

Yes. Feather Falling conflicts with neither water enchantment.