My daughter has recently turned 4 and was raised in somewhat the same way. We speak Dutch to her, but she sees a lot of English videos and stories, so she also picks up some Dutch.
She started making proper sentences shortly after she turned 3 and is currently doing quite well. She occasionally mixes English and Dutch words and understands that they mean the same thing.
However I feel it is important to point out: what you are describing is not bi-lingual education. My daughter cannot make English sentences, because she does not have enough experience speaking the language herself.
She has a friend who is being raised fully bilingual, but that means the parents actively engage the child in English conversations, as do his teachers. The result is that he (at 5 years old) can hold full English conversations and build English sentences, which is something my daughter cannot keep up with.
So don't feel it's strange that she will only start building Czech sentences with the occasional English word intermixed; I think that is to be expected if your only contact with English is from video/audio.
The answer for this is essentially the same as it is for monolingual (and polylingual) children.
While each individual is unique, the advancement to the use of full sentence structure, as opposed to isolated words, arises from how the individual is exposed to language. In the first years of life, everything is new, so the brain is in constant learning mode. Even in infancy, before children ever begin to articulate speech, they are constantly watching, listening, feeling, tasting.
When parents commit to always using the same speech patterns when talking to their children as they use in everyday conversation with adults (i.e., full sentence structure;1 not using "baby" versions of words like "choo-choo" for "train";2,3 not intentionally mispronouncing words in an imitation of the common mispronunciations children often make, e.g., "brush your teef", "watch dis", etc.4), those children tend to speak in complete sentences themselves at an earlier age; learn words, grammar, and syntax more quickly; and generally develop their communications skills more readily; than do children of parents that take the opposite approach.
For multilingual children, this concept can simply be extended to account for the degree to which they are exposed to each language. If the parents speak one language natively and a second language less than fluently, the child will tend to become far more fluent in the first language, unless also exposed to the second language by other speakers that are fluent. If exposed to full sentences in the first language, and mostly isolated words in the second, they may more easily integrate those words into their speech than the parents do, but will tend to only use the syntactical structure of the first language, in terms of phrasing, clause separation, etc.
So for the specific case here, the best way for a parent to promote the use of full sentence structure is to commit to always using full sentences themselves when speaking to (or around!) the child. Obviously, to teach specific words you'll need to place focus on those words individually, but make efforts to always integrate those new words into full sentences as much as possible.