Daniel

I thought it might help if you could hear (and then repeat) my Canadian pronunciation of each of the words in your list.

- shit sheet beach bitch bird beard

I pronounced each word twice (so you can stop the recording and try to copy the sound).

My standard Canadian accent is similar to a standard Amercian accent.

https://vocaroo.com/i/s1g3utBqoGqf

Worry the right amount. Try to learn how to hear and say the two different vowels, but don't worry about it too much.

On the one hand, they do sound different to English speakers. Someone could ask me to take dictation, and if they used the words "bitch" and "beach" I would probably pick the correct one 90% of the time or more.

I am not surprised to find that you are a Spanish speaker. Spanish only has five vowel sounds; English has about twelve simple vowels and eight to ten diphthongs. Imagine the Spanish "i" as including a range of sounds that are close enough to a perfect "i" that you hear them all as "i." Well, unfortunately, the two different vowel sounds in /bɪtʃ/ and /biːtʃ/ both fall within the range of the Spanish "i" sound, and you hear them as "the same."

You will just need to train your ear to hear the difference. Perhaps this website will help:

http://soundsofspeech.uiowa.edu/resources/english/english.html

On the other hand... this is important... most of the time, in context, you will not be misunderstood. If you ask someone "Can you give me directions to Revere Bitch?" most listeners will actually think they have heard "Revere Beach." If someone is teasing you about your accent, they may pretend to misunderstand, but in reality they will know what you've meant. In all languages, we hear from context, and we hear "the closest thing that makes sense." It is a good idea for you to tune up your ear, and then, when you hear the difference your pronunciation, but it is not the most important thing, and in real life people will not be offended by mistakes.

Those words sound very different, and you are right to be concerned -- you want to prevent misunderstandings. A long while ago a student tried to tell me about his trip to the U.S. but was also unclear on the pronunciations of the words "beach" and "bitch." 

Student: When I was in America, I was with a lot of sandy bitches.

Me: Do you mean that you had dates with a lot of women with blonde hair?

Student: No. There was a lot of water, and a lot of sand.

Me: Oooh!!! You went to a lot of sandy beaches!

Student: Yes
Me: Ok. Let's practice the words "bitch" and "beach" so we can keep you safe in America! :-)

Just remember the following:

shit -- short "i" sound (sounds like spit)
sheet -- long "e" sound (sounds like heat)
beach -- long "e" sound (sounds like each)
bitch -- short "i" sound (sounds like itch)
bird -- pronounced berd (sounds like herd)
beard -- pronounced  beerd (sounds like weird)

Say these words slowly and exaggerate their pronunciation until you get it right. Pay attention to how your lips move when you say them. Just practice -- You'll get it. :-)

No, they do not sound the same at all.

I will group them together for you so you know which sounds are the same.

$h!t and B!tch both have the same vowel sound.

Sheet and beach both have the same vowel sound.

Bird has a different vowel sound. It rhymes with the word "heard".

Beard has a different vowel sound. It rhymes with the word "weird".