Learn Hardcore Russian: Летом я чаще езжу на велосипеде, чем на машине. - In summer I ride a bicycle more often than a car.

Летом is the instrumental form of лето used adverbially to mean “in (the) summer”.
For seasons and some times of day, Russian often uses the bare instrumental without a preposition:

зимой – in winter
весной – in spring
осенью – in autumn
ночью – at night

You do not say в летом. You can say летом, or more formally/precisely летом, летом месяцы, etc., but the basic everyday form is just Летом = “In summer”.

Why is the verb езжу and not еду?

Russian has two basic verbs for “to go (by vehicle)”:

ехать (я еду) – one direction, one concrete trip, “I am going / I’m on my way (now).”
ездить (я езжу) – multi-directional or repeated/habitual trips, “I (usually) go / I travel (by …).”

In this sentence we are talking about a habit: what I usually do in summer. That’s why the multi-directional ездить → езжу is used:

Летом я чаще езжу на велосипеде… – “In summer I more often (tend to) go by bike…”

Does езжу describe present or future? How should I understand its tense here?

Formally, езжу is present tense, imperfective aspect.
In practice, with an adverb like летом (“in summer”) it describes a general, repeated habit, not a single moment:

“In summer, I (generally / usually) ride my bike more often than I drive.”

It can also include a near-future sense (“this coming summer I do/usually do X”), but grammatically it’s present habitual.

Why is it езжу на велосипеде and not something like езжу велосипед (with a direct object)?

In Russian, when you say you travel/ride using a vehicle, you normally use на + Prepositional case, not a direct object:

ездить на велосипеде – to go (around) by bicycle
ездить на автобусе – to go by bus
ездить на поезде – to go by train

So велосипед is not the thing you are “doing” or “acting on”; it is the means of transport. That’s why the pattern is ездить на + (Prepositional), not ездить + Accusative.

What case is велосипеде and why does it end in -е?

Велосипеде is Prepositional singular of велосипед.

Nominative: велосипед (bicycle)
Prepositional: о велосипеде / на велосипеде

Masculine nouns ending in a consonant usually take -е in the prepositional singular.
It’s in the prepositional because of the preposition на (“on / by” here).

Why does Russian say на машине for “by car”? That looks like “on the car.”

With means of transport, Russian almost always uses на + Prepositional:

на машине – by car
на автобусе – by bus
на метро – by metro/subway
на самолёте – by plane

Literally it’s “on the car/bus/plane,” but in Russian this is the normal, idiomatic way to express “by [vehicle]”.

Compare:

Я еду на машине. – I’m going by car.
Я сижу в машине. – I’m sitting in the car.

На focuses on the method of travel.

Why is there a comma before чем?

Here чем introduces the second part of a comparison:

…я чаще езжу на велосипеде, чем на машине.
“…I ride my bike more often than (I go) by car.”

Grammatically, the second part is an elliptical clause:
(чем я езжу) на машине – the verb езжу is understood and omitted.

In comparisons of this type (comparative + чем …), Russian normally separates the two parts with a comma. So the comma before чем is standard and correct here.

Why isn’t the verb repeated after чем, like чем езжу на машине?

In Russian, it is very common to omit repeated verbs in comparisons when they are clear from context:

Я чаще езжу на велосипеде, чем (езжу) на машине.

Repeating езжу is grammatically possible (чем езжу на машине), but it sounds heavier and less natural in this specific sentence. The short version with omission is what people say in everyday speech.

Could I move чаще somewhere else, like Летом я езжу на велосипеде чаще, чем на машине? Is that still correct?

Yes, that word order is also grammatical:

Летом я чаще езжу на велосипеде, чем на машине.
Летом я езжу на велосипеде чаще, чем на машине.

Both mean the same thing. The usual and slightly more natural option is the original one, with чаще closer to езжу at the beginning of the predicate, but Russian word order is flexible and both versions are fine.

What is чаще exactly? Is it an adjective, an adverb, and can I say более часто instead?

Чаще is the comparative form of the adverb часто (“often”):

часто – often
чаще – more often

You can say более часто (“more often”), but for simple comparisons of frequency, чаще is much more natural and idiomatic.

Examples:

Я чаще читаю по вечерам. – I read more often in the evenings.
Он чаще ездит на работу на метро. – He more often goes to work by metro.

Why don’t we say мой велосипед or машину with some article meaning “the/a”? How do I know whose bike or which car it is?

Russian has no articles (“a / the”), and possessives like мой, твой, его are used only when needed for clarity or emphasis.

In a neutral sentence like:

Летом я чаще езжу на велосипеде, чем на машине.

it is naturally understood as “my bike / my car” (or just “a bike / a car” in general) from context. Adding мой велосипед or моей машине would only be necessary if you specifically wanted to contrast possession, e.g.:

…чаще езжу на своём велосипеде, чем на папиной машине.
“…I more often ride my bike than my dad’s car.”