library(tidyverse)
#generate some data
rerun(10, iris) %>% 
    walk2(str_c('df', 1:length(.)), ~assign(.y, .x, pos = .GlobalEnv))
map(str_c('df', 1:10), ~ eval(sym(.x))) %>%
    reduce(bind_rows) %>%
    as_tibble() #to avoid console flooding
#> # A tibble: 1,500 x 5
#>    Sepal.Length Sepal.Width Petal.Length Petal.Width Species
#>           <dbl>       <dbl>        <dbl>       <dbl> <fct>  
#>  1          5.1         3.5          1.4         0.2 setosa 
#>  2          4.9         3            1.4         0.2 setosa 
#>  3          4.7         3.2          1.3         0.2 setosa 
#>  4          4.6         3.1          1.5         0.2 setosa 
#>  5          5           3.6          1.4         0.2 setosa 
#>  6          5.4         3.9          1.7         0.4 setosa 
#>  7          4.6         3.4          1.4         0.3 setosa 
#>  8          5           3.4          1.5         0.2 setosa 
#>  9          4.4         2.9          1.4         0.2 setosa 
#> 10          4.9         3.1          1.5         0.1 setosa 
#> # … with 1,490 more rows
#if all the df's are inside a list
data <- rerun(10, iris)
reduce(data, bind_rows) %>% 
    as_tibble()
#> # A tibble: 1,500 x 5
#>    Sepal.Length Sepal.Width Petal.Length Petal.Width Species
#>           <dbl>       <dbl>        <dbl>       <dbl> <fct>  
#>  1          5.1         3.5          1.4         0.2 setosa 
#>  2          4.9         3            1.4         0.2 setosa 
#>  3          4.7         3.2          1.3         0.2 setosa 
#>  4          4.6         3.1          1.5         0.2 setosa 
#>  5          5           3.6          1.4         0.2 setosa 
#>  6          5.4         3.9          1.7         0.4 setosa 
#>  7          4.6         3.4          1.4         0.3 setosa 
#>  8          5           3.4          1.5         0.2 setosa 
#>  9          4.4         2.9          1.4         0.2 setosa 
#> 10          4.9         3.1          1.5         0.1 setosa 
#> # … with 1,490 more rows
Created on 2021-06-25 by the reprex package (v2.0.0)
Edit: An alternative way using !!! (bang-bang-bang).
.args <- str_c('df', 1:10) %>%
    map(~eval(sym(.x)))
bind_rows(!!!.args) %>% 
    as_tibble()
#> # A tibble: 1,500 x 5
#>    Sepal.Length Sepal.Width Petal.Length Petal.Width Species
#>           <dbl>       <dbl>        <dbl>       <dbl> <fct>  
#>  1          5.1         3.5          1.4         0.2 setosa 
#>  2          4.9         3            1.4         0.2 setosa 
#>  3          4.7         3.2          1.3         0.2 setosa 
#>  4          4.6         3.1          1.5         0.2 setosa 
#>  5          5           3.6          1.4         0.2 setosa 
#>  6          5.4         3.9          1.7         0.4 setosa 
#>  7          4.6         3.4          1.4         0.3 setosa 
#>  8          5           3.4          1.5         0.2 setosa 
#>  9          4.4         2.9          1.4         0.2 setosa 
#> 10          4.9         3.1          1.5         0.1 setosa 
#> # … with 1,490 more rows